Why is it so hard for people to concede even small points when discussing charged topics?

The backfire effect. Here's a nice funny comic to explain it. https://theoatmeal.com/comics/believe

You will realise that many people are too egotistic to back down.

Also consider the Yes Ladder - in sales, getting someone to say yes to something small makes them more likely to agree to other things.
It also applies to other contexts. If a police suspect refuses to talk, they ask innocuous questions because once someone starts talking, it's hard to stop.
Admitting incorrectness will make you more likely to concede other points too

I think we have an ecolutionary predisposition to be very defensive when we feel threatened. Add that to a social environment where we are CONSTANTLY and artificially condititioned to be threatened, considering that emotional intelligence and the ability to articolate and understand your own thoughts (let alone other's) are virtually never taught if not en passant and indirectly (and often the wrong this are taught) and you have the perfect recipe for the Tower of Babel.
Humankind's inherent incommunicability of internal thought is paired with an artificial and political cooptation of our survival instincts, the ones we evolved to defend ourselves from the people that a re manipulating us right now. That's the reason antiauthoritarian thought is often patologized. They name the cure a sickness so that we keep ourselves under the Veil
- I think I see what you’re trying to say, and I don’t necessarily disagree with everything, but based entirely on this one comment (which may not be indicative of how you generally communicate) I have to wonder if the communication issues you see stem at least partially from your own over-articulation of thoughts and use of “fluffy” language.
  I think this bit highlights what I’m trying to say best:
  are virtually never taught if not en passant and indirectly This statement feels like it’s saying the same proposition three times, but if I dig into it it is saying three things, but in a confusing manner. I think it would have been better served by replacing “if not” with something simpler like “or taught” to more easily connect the first idea with the other two in the reader’s mind. I probably would have replaced it all with “are taught incidentally at best,” which I think captures the meaning you are trying to convey in terms that are easier for anyone to understand.
  I don’t say this to try to bring you down. I just find beauty in seeing a concept existing in one’s mind, unbounded by the world, given a vessel structured by the words of language not to constrain or limit that idea, but to focus it into something that can be shared and understood with others. The vast majority of the time I see that vessel be too loose without giving proper shape to the idea it wants to convey. Yours is one of the very few internet comments I see that does the opposite, where it feels forced into a shape that’s too rigid. That makes me want to say something, because the mind that does that is a mind I think could learn from stepping back a little, rather than being told to force itself forward.
  This is as much me challenging myself to understand what bugged me about your comment as it is a comment on your comment, and for talking about giving shape to thoughts I don’t think I did a super job of it.
  I do think that humans are one of the only creatures capable of overcoming the difficulty in communication between minds because we are one of the only creatures capable of complex language to do that stuff I said earlier. But it is a skill that is difficult and requires a lot of time and effort to learn or teach. I do think communication is highly valued, or at least a lot of frustration espoused about a lack of communication, but modern society does make it difficult to work up the effort and acquire the resources to develop that skill.

Read up on cognitive biases.
People are social animals. We form groups and we stick with them. Some of our cognitive biases are very clearly geared toward preserving the cohesion of the group. The truth is very much secondary to group cohesion.
Individuals vary a lot, however. And some individuals are much more open to changing their mind than others. Groups are stronger when they have a variety of different personalities within them. Different people can have different roles within the group and help it adapt to changes.

If you're genuinely interested, then there are people studying and talking about this (beyond the expertise of Lemmy). There's a fantastic podcast I listen to that talks in detail and there author has written a book about how minds change. Here's a specific episode (out of many) that is relevant, but I would really recommend listening to all:
https://youarenotsosmart.com/2022/05/01/yanss-231-why-we-often-cant-choose-what-we-believe-thanks-to-the-fact-that-certainty-is-a-feeling-and-not-a-conclusion/

I'm not an expert, but…
even when doing so wouldn’t necessarily undermine their broader position
Conceding one wrong is proof that you, your view or argumentation, is flawed. Conceding just one minor point puts every point's validity into question.
Even if you can conclude that it's irrelevant both factually there's social and emotional aspects to it.
We are driven not only by reason, but in large part by emotion, and our ingrained social psyche.
Even if it is factually irrelevant, conceding is confirming fault, and may cause anxiety about repercussions in terms of social standing (how you are seen by the others) and for your argument as a whole (will you be trusted when something you said was wrong).
What you describe as building identity is building that identity around a set of beliefs and group of people.
Depending on the group and beliefs, two aspects come into play:
Group dynamics of in-group and out-group. Loyalty may be more important than reason. The own group is likely seen as better than the "others". Others may be seen as inferior or as enemies.
If you acknowledge just one point integral to the groups beliefs, what does that mean for you as a part of that group? Will you lose all your social standing? Will you lose being part of the group?
Somewhat unrelated and related at the same time, because self-identity is also a construct to build stable group associations; building your confidence and self-identity around a set of values, conceding on some of them means losing stability and confidence in yourself, your worth.
The human psyche is still largely driven by genetics developed in ancient times, and the environment.
As a social create, it was critically important to be able to join groups and stay in them, to have strong and stable bonds. This persists today, in our psyche and behaviors.

It can feel a bit lopsided - if I'm having a conversation about some divisive thing, and grant a point, even a small one: the other person will probably keep harping on the thing I was wrong about. Meanwhile, that person will never admit they were wrong about anything.
It's a symptom of treating these conversations like debates. After you 'lose' a couple, you're conditioned not to give an inch.

Very often on Lemmy, and maybe social media in general, discussions are pointless. People are not there to see the other side, they are there to fight for what they already think.
All these keyboard warriors think they are fighting a battle, weather its about defending trans rights or fighting antivax opinions, or whatever.
- The discussion usually is for the benefit of lurkers and rarely results in changing the opinion of the opponent.
- This is all true. it's something that crosses my mind whenever I spend (i.e. waste, probably) any time at all in debate. In person too, BTW, although text feels even worse because of the way it disembodies your interlocutor.
  And yet. Open debate is all we have. The alternatives cannot possibly be better. I tell myself that even if 99% of it is useless, that remaining 1% can make a lot of difference statistically. I can certainly think of occasions when I've changed my mind, or at least seen things in a new light, because of a single comment someone made in debate. But yes, it's rare.

I dunno, man.
All I know is that open-mindedness is far less common than I’d once assumed.
And there are those people who aren’t actually interested in truth, but are instead interested in “winning,” because they see every conversation as a power struggle, with a winner and a loser (and as such, language is merely a tool to be wielded for gaining and maintaining social power, not actually finding out things for their own sake). Part of that game can include pretending to be curious and interested in truth, because of the positive image that can project for them.
When those of us who are actually curious about the world interact with one of these types, it can be quite a confusing and frustrating experience if we don’t know what we’re dealing with.

Lemmy is worse than reddit in almost every measureable way. The reason I haven't gone back to reddit is purely out of principle and it's not a principle if it's not costing you anything.
Damn your opinions suck lmao. Were you the reason Blahaj defederated from feddit.uk?
Cuz it would be funny if one user could annoy a community so much that they decide to defedreate the entire instance.
Also the above comment being right next to:
Longest continuous edging streak. Hell, I might already hold that record anyway.
Perfect example of a reddit user lol.
- What do you get out of going around insulting complete strangers? People being intentionally mean online is honestly baffling to me.
  
  what's baffling is that you don't see it!

Oh boy. If you really wanna understand this, there are like 80 episodes of the podcast You Are Not So Smart that look at this from different angles.
There’s not really a single reason. It’s a lot of inter-related ones.

I'm not here to rehash any particular political event or take sides
checks post history out of curiosity oh.
- Their name should give away that they are a troll.
  
  the irony of their position and still asking this question is military grade, ironically enough in its own way.
- To quote myself here:
  I’ve also noticed that criticism toward one side is often immediately interpreted as support for the “other” side, leading to tribal reactions rather than nuanced thinking.
  
  mmhmm, keep going...

Because I am always right obviously

Hmmm. There are a lot more opinions about this than I thought there'd be.
Personally, and without any real evidence? I think it's just because conceding a point somehow feels as if it compromises your whole position. Like you're getting scored, and admitting you're wrong gives the other person a point and undermines your entire argument.

For example, it feels like many people bind their identity to a cause so tightly that admitting any fault feels like a betrayal of the whole.
That's exactly it in a lot of cases. More on that here:
https://www.paulgraham.com/identity.html

Probably cause kids ridicule you hard if you are wrong or stand out. When you grow up, you might learn to have your own opinions, but you might never unlearn the various defens mechanisms and feelings of ridicule that developed as a result of kids around you scrutinizing you and your opinions.
They don't want to hear it cause it is uncomfortable. And they feel like they are loosing respect and getting attacked. They rather sweep it under the rug and forget about it, sometimes not learning from it at all. Humans are also lazy.
Being wrong gracefully is a learnt skill.

One thing I would add to all the good answers here: It stems from a lack of contact with real-world, messy, difficult environments.
Usually people who come into contact with harsh reality a lot in their daily life are pretty humble. They don't get stuck on one way of looking at things, they don't refuse to admit obvious good sense arguments. Even if they get to the point that they're super-qualified, they just kind of have common sense and are approachable. Mostly, not always. I think this is why people kind of fall in love with certain types of environments with a lot of challenge or "win or lose" aspect to them: Business, sports, law, war, esports, mountain climbing, whatever. It's like you get to prove yourself and all your bullshit against the harsh light of day, and a lot of times what you learn is that some genius theory wasn't really all that solid once it got exposed to the real world.
But then, a whole lot of first-world modern life isn't like that. You can just go around your entire life talking about economics or politics and just be wrong as hell and you never get to find out. So it's easy to be super-confident, and it's obviously a lot more comfortable to be always right about everything than it is to admit when someone's maybe successfully poking a hole in your genius.

In general the small points are not actually related to the overall point or are the rare exception to larger trends and are either meant to derail the discussion or show that the other person is going for gotcha points.

I think it sometimes depends on how much they have internalised their perspective on a topic as a core part of their personality.
If they perceive a disagreement with their perspective as a direct attack on their person, that can lead to subjectively bad outcomes.
There is also the possibility that what you see as a small point is a critical point to them.

Because team mentalilty.
Many people will instinctively disagree just because you happen to be on the other team.
Let's take political ideologies, they all want the same thing:
Good schools, good healthcare, good geriatric care, good infrastructure and so on.
Where they differ is how they get there.
The left want the government to provide these services, the right want the private sector to do it.
To have a productive discussion on how to solve society's problems, I find it better to talk about the issue itself and avoid branding yourself as a part of a particular movement.

You have to do the heavy lifting, not them IMO.
For example the why should we help lazy people?!! I wonder what should we actuallydo with them then? Like you're too lazy to work should we let them die because of their "stupidness" and errors they made?
Never changed anyone's mind right away but you get to talk about the underlying reasons why they hate "lazy" people, and it's often something (shocker) that has nothing to do with "lazy" people.
For example.
Edit: I use the rightwing trope here just as an example. I'm the laziest person I know!
- I'm not convinced 'lazy' people exist. Everyone I've ever known to be lazy is either ADHD, depressed, or anxious. It's a symptom of an unhealthy mind, not an inherent trait anyone possesses.
  
  This is my experience as well. Anecdotally, at least. Lately I've been slowly putting together a community of friends, and my anxiety and depression have been dropping like crazy. Between that and the self-esteem boost I've been getting from finally starting hrt, I'm actually starting to feel competent enough to tackle things like getting a job, moving out (I'm gonna go looking at rental properties with a friend tomorrow), going grocery shopping, things like that.
  God, I've always wanted to be able to just do something so plain as going grocery shopping for myself.
  I can also tell that the anxiety causes a lot of issues with my motivation from the fact that my wonderful mom always throws worst-case scenarios at me whenever I try to become more independent. She's been throwing the entire warehouse at me lately because I've been talking about how I'm moving out with a friend. My excitement has been turning to dread despite my friend's reassurance that they'll catch me if I fall; and as a result my motivation and ability to get out of bed has been plummeting.
  But... Yeah. Anecdotally, it's not laziness, it's being anxious, overwhelmed, overstimmed, depressed, feeling lonely (I mean, what's the point in doing anything if no one cares?) and so forth.
  
  Totally!
  I just used the classic "lazy beggar don't want to work" rightwing trope here.
  
  For sure. From my experience of having kid on spectrum, dealing with it and learning about how to help him (ok, the wife did most of the work there), we came to conclusion that almost all people have either ADHD or autistic traits, some even both. People we know that have ADHD traits are almost all a mess, add some shitty parenting or being prone to addiction and you have a recipe for disaster.

It depends a lot in which context the "discussion" is taking place.
at a dinner table it's more about small talk and performing... "social grooming" as you would observe it in ape societies.
at official events, people either have a job or an established opinion, they are in a stressful environment that does not actually allow them to make rational evaluations
in school / academia / media, the particular response and opinion will affect your grade, social standing and future career opportunities
In all of those situations, it should be obvious why the "dominant" position does need to give an inch, for social reasons.
Even in absolutely perfect conditions, calm environments, prepared discussion participants, "objective neutrality" towards the outcome, individuals will have different opinions on importance of topics or methods and will discard "details" or see them as irrefutable counter examples.
Basically, there are lot of (subconscious) things going on that prevent an "objective discussion" from happening. I'm sure you can find specific examples of what could be influencing people in specific circumstances once you look for them.

People are very reluctant to admit they're wrong in general. If you then have an emotional connection to the topic, even more so.

Hot take: Lack of world-shattering psychedelic experiences.
Regular take: media designed to isolate or at least divide. Plus general trend of less in person daily contact

People will rather justify doublethink than admit they are wrong.

Because that would shatter their worldview which is essential to how they understand the world and themselves in it.

Because it conflicts with their personal identity. If I point out being “pro-life” while also denying people’s right to health care for that life is hypocritical, I’m calling you a hypocrite from your perspective.
- I can't help myself but to comment on this though it gets a little off-topic.
  I think the "pro-life vs healthcare" example can be a little more complicated.
  If someone sees abortion as equivalent to murder (because they believe life begins at conception), their opposition is based on a direct moral prohibition - being against killing - rather than a broader stance on care or social services.
  That doesn't mean there aren’t inconsistencies elsewhere, but the perceived contradiction might not be quite as direct from their point of view as it sounds.
  
  abortion as equivalent to murder
  They don't believe that. They think they believe that, but they don't. The frozen embryo in the fire question proves this. The fact that they aren't actively killing abortion doctors proves this.

Pride and ego

I'm sure there's a trove of psychology research we could look through instead of speculating

- To admit that you’re wrong would be to admit that your view is the weaker one.
  Perhaps I'm playing in to the scenario OP is describing but I'd argue that being wrong (let's assume for this example it's provably, objectively wrong) isn't necessarily weakness, sometimes it's just incorrectness.
  i'm possibly drawing a pedantic line between weakness (a potentially valid, but weaker argument) vs incorrectness ( an argument that is provably, objectively incorrect ).
  Perhaps i'm just describing the difference between subjective and objective arguments ... hmmm, not sure

Because people go into these debates online to prove themselves right. They have no intention from changing their opinion from the begining. They only want to prove the others wrong. They have already a defense build up that discredits whatever others says. They don't care about communication or understanding others they only care about representing their opinions the best way possible. Worst part, the harder they "lose" these debates, the deeper their believes in their opinion grows as they feel the need to defend their believes.
As a tip, if someone wants to debate you on a topic, don't engage or engange in a communicative & cheritable manner trying to understand them and why they hold their believes. Try to move their opinions a little from their side "I get exactly what you mean, but how abou this and that. Have you considered these possibilities?" Let them reach the right conclussion and not you force them into a conclussion. I know it's way harder than just straight up debating them but way more productive if you truly care about a topic and want to engage with them in a debate.

I think it's two things.
Tribalism and identity play a large role here, we're wired to defend our identity and that of our group so we naturally get defensive when those things are questioned.
We have cultivated a culture in which being wrong or changing your mind about this stuff is weakness or makes you a bad person.
People are desperately afraid of being wrong, of admitting that they made a mistake, especially one that makes them question their tribe's values because that combines shame and judgement with the possibility of being ostracized.
Personally I've always tried to cultivate a willingness to be wrong because I value having the best possible information more than not being wrong or questioned. I actively seek our situations where my core beliefs and opinions are challenged and tested, where I am exposed to new ideas and perspectives, because to me that is the only way to make sure I have an accurate and well informed worldview. But it definitely took a lot of effort to quash that gut reaction of 'fuck you don't question me'.
- It’s been less than a week since I last publicly admitted to being wrong about something. Not only did I get called ignorant for being wrong in the first place, but even more so for admitting it.
  I also agree with your point about pressure-testing your own beliefs. Whenever I’m debating someone, it’s as much about trying to influence their beliefs as it is about letting them test mine. I know I’m wrong about plenty of things, and I don’t want to stay wrong any longer than necessary. If there’s a flaw in my reasoning, I want someone to point it out to me in a way I can’t ignore.
  It’s painful to be proven wrong - I’m not immune to that either. It stings. What I don’t understand, however, is why, instead of simply leaving the discussion, some people start making excuses, redefining terms, rewriting history, or attacking me personally based on beliefs I often don’t even hold. That kind of behavior just seems absurd to me.
  I’m usually not someone who picks sides easily, but I think the Russian invasion of Ukraine is a rare example where it’s pretty clear to me who the good guys are (though I’m open to counterarguments). Even then, if someone pointed out that Ukraine has committed war crimes too, I’d say that’s almost certainly true - but it doesn’t change how I feel about Ukraine broadly when compared to who they’re fighting against. My worldview isn’t threatened by admitting that. I genuinely struggle to understand the perspective of someone who can’t do the same.
  
  One nice thing about being willing to admit that you're wrong is when other people make a big deal about it you can say something like 'Look, I apologized and I said I would do better in the future, are you trying to accomplish something with all this endless harping on a resolved issue or are you just still stuck on how upset you were that I'm fallible just like everyone else?'
  I don’t want to stay wrong any longer than necessary
  Right, exactly. I care more about having the correct information than I do about being seen to be right. Honestly I don't find it painful to be wrong unless it's something I defended eagerly and resisted being corrected on, which does happen sometimes, but most of the time I can just shrug and go 'My bad, but at least I've learned something here today.'
  What I don’t understand, however, is why, instead of simply leaving the discussion, some people start making excuses, redefining terms, rewriting history, or attacking me personally based on beliefs I often don’t even hold. That kind of behavior just seems absurd to me.
  Because some people over-correct in resisting being wrong until they have to be right all the time.