Full Circle

Specifically the second one.

immigrate from Europe

emigrate to Europe

Depends on your viewpoint.
Emigrate from Europe and immigrate to Europe is also a valid way to look at it.
- It is, but that's not the viewpoint they used in the meme
According to Etymonline,
Immigrate = in- "into, in, on, upon" from PIE root *en + migrare "to move" from PIE root *mei
Emigrate = assimilated form of ex- "out" from PIE root *eghs + migrare "to move" from PIE root *mei
So I guess to correct usage would be:
Immigrating to Europe/US
Emigrating from US/Europe
- It depends on where you're speaking from.
  If you're in the US, people were immigrating from Europe and to the US and are now emigrating to Europe and from the US.
  If you're in Europe, people were emigrating from Europe and to the US and are now immigrating to Europe and from the US.
  Easiest solution is to say migrating :)
  
  people were immigrating from Europe
  The linguistically correct term her would be emigrating from Europe.
  to the US
  This is immigrating.
  emigrating to Europe
  This is immigration.
  from the US
  The word you're looking for is emigration.
  emigrating from Europe
  You're correct here.
  to the US
  Once again, immigration.
  immigrating to Europe
  This is the linguistically correct use of the term.
  from the US
  Proper word would be emigrating.
  Easiest solution is to say migrating
  Migration by itself doesn't indicate whether you're referring to domestic-only movement, where people migrate inside of a country, or domestic-to-foreign where they cross a border, or foreign-to-foreign movement.
  It all depends on the boundary you set.
  If your chosen boundary is Europe, people moving to Europe are immigrating there, and people moving from Europe are emigrating there.
  If your chosen boundary is the US, immigration is moving to the US while emigration is moving from the US.
  Since migration isn't specific and can refer to any of the above cases, I prefer transmigration since "trans-" refers to "across" which I often interpret as "out from and in to".
  We don't need to give up on prepositions in order to have more accurate language.
  
  This is way too confusing for me to follow but it sounds vaguely like we mean the same thing.

i think you use "emigrating" when leaving their homes behind, but here it is part of the joke that they no longer see the US as their home. instead, they're seeing europe/whatever other country as their new "home", so they're immigrating.

Do you imagine some kind of deeper meaning wrapped in a joke in it?
The more likely explanation is that plenty Americans have poor literacy.
Even plenty of 'their' 'there' mistakes. Elemental English.

Just my two cents, not having a go at you:

This is why I'm a pragmatic prescriptivist, I want people to follow norms for ease of communication, unless their innovation fills a need/fixes something about the language.

Stupid english with its stupid verbs.

We've got "to" and "from" why do we need to have two differently spelt verbs for basically the same thing.

Sure, you could argue that you can just say "they are emigrating" to imply people are leaving the country permanently, but let's be honest, not providing any other context it's practically unheard of. You'll at least be saying where they currently are, came from, or going to, unless you're being very abstract. Even then, you couls say "the migrants were immigrating" to be very vague about it. Both immigrating and emigrating involve moving, wtf is the point?

I'm glad few people "properly" use "emigrate" these days. Let's kill it, it's redundant!

I may have even gotten the difference wrong, but I'm not gonna look it up since I don't want to use it anyway haha

I, personally, like a language being rich. Nothing wrong with not knowing all the ins and outs, but calling for simplification on what is already an very simple language is odd.
- I just have to point out, in an argument about language pedantry,
  an very simple language
  
  Point taken :D Coffee must kick in at some point.
- I wouldn't call English simple haha
  To me the richness comes from interesting cultural quirks of why we say something, but I'm not really feeling that for emigrate, personally, so would prefer we speed up it being forgotten. Words falling out of use is very common, so I'm happy to lose ones that are annoying
  I should also specify, I'm just getting into the spirit of enjoyable nitpicking, also
How about just 'migrate' and 'migrating'?
- In my view, "migrate" according to Etymonline originates from the Proto-Indo-European (PIE) root *mei which means "to change, go, move".
  I don't believe this term refers to moving in or out of something, or any other preposition.
  As we've been discussing in this post, immigrate and emigrate represent inverses of each other. It makes sense to look for logical ways to combine those.
  I think the best prefix for this would be trans- for, according to Etymonline, this means "across, beyond, through, on the other side of; go beyond". Specifically, I would refer to trans- as meaning "out from and in to", which gives us the word "transmigrate". Etymonline has a dictionary entry for "transmigration".
  It looks like Merriam-Webster, Oxford, and American Heritage dictionaries support "transmigrate" as an entry.
  
  From wiktionary: Verb migrate (third-person singular simple present migrates, present participle migrating, simple past and past participle migrated)
  (intransitive) To change habitations across a border; to move from one country or political region to another. To escape persecution, they migrated to a neutral country.
  This is already common usage and I don't see the need for any prefixes to the word. The Etymonline definition is giving the definition of the root, not the current english word.
  
  This is already common usage and I don't see the need for any prefixes to the word.
  As we've already seen in this thread, sometimes prefixes are needed to help establish the arrow of causation when people do migrate. Did they come to or leave from this or that country? Etc.
  not the current english word.
  Good thing language can change over time :)
  
  The problem we're addressing is that the prefixes are made redundant by the syntax of to and from. 'immigrating to europe' 'emmigrating from europe'. Dropping the prefix in this context doesn't change the meaning: 'migrating to europe' 'migrating from europe'.
  
  I agree. Maybe immigrating Europe or emigrating the US, but that does seem odd.
- But this is the digital age, so it's clearly e-migrating.
I think there's a richness in being able to shift or emphasize perspective like that. And a poetry, for want of a better word, that comes with that.
'Coming' and 'going' do the same shift. "I'm coming to Europe; they're coming from Europe," feels just a bit stilted to me, though that's subjective I suppose.
If you want to get rid of immigrate Vs emigrate, maybe we just talk about 'migrate'.
And scrap 'coming' and 'going' for 'moving'.

But only in the first sentence