The most difficult argument to argue against against the death penalty is that you cannot repair for the damages of executing a person you've wrongly convicted, if new evidence appears too late.
This doesn't even mean there aren't people who deserve to die, or who deserve suffering. Rather, it's an acknowledgement of the fallibility of human institutions.
That's why death penalty shouldn't exist for crimes like a wife killing a husband. You might be 99.9% sure she poisoned him, but you cannot know for sure.
However, a school shooter caught red handed shooting a school?
Some crimes and scenarios can warrant the death penalty in my mind
Next argument is "what if the government framed people to execute them?"
Why in the world would the government point out that they are executing someone?
If the government (the rich controlled government) wants you dead they would do it quietly.
Even something as simple as cutting your brake lines. You really think local police are going to figure out that the government had soldier 65478 tamper with your brake lines?