The fact that you think there is a justification for wanting someone dead is what's wrong in the first place, and is the entire reason the capital punishment exists.
There are objective facts that support abolishing the death penalty, such as:
-life in prison is cheaper
-the justice system isn't perfect, and we've executed innocent people before
And we can stop there.
The only "evidence" that pro-death penalty supporters have is that it's some sort of primal notion of justice, even though society, the victims of the killer, and the family of the victims gain nothing from it.