If you bake bread, you are a bread baker. If you play football, you are a football player. If you murder someone, you are a murderer.
If you don’t commit the crime of murder, you are not a murderer. Murder is a legal term. Administering a death penalty is not murder, since it is not a crime.
No matter how much batman says otherwise, there is nothing inherently not ok about death penalty for murderers. Of course, you can dislike it all you want. But don’t go slandering people that disagree with you.
Arguably, the opposite is true: If I decide I really want to kill you, what should be the minimal punishment? Is it ok to just pay a fine? Is it ok to be in prison for a month? How about a year? What if I decide the slap on the wrist punishment is worth it? Why should the punishment be less than paying with my own life in kind? Why is your life worth less than mine when I am the murderer in this hypothetical?