"You have wronged me," —done something that contradicts my beliefs are hurts me in any way "so therefore I shall deprive you of your life and put you out of mine."
The only good thing about putting criminals on death row is clearing more space in the jails for more criminals, and putting them out of one's own life. Dying doesn't cleanse anyone of anything, does it? it may make them regret, that's for sure; but does it make them see the "error" of their ways? Does it help undue any of the "harm" this criminal has done? No, not really in my opinion... i'd rather let them live and study them, as a scientist who study's an animal's behavior—er, no, that's wrong— like a psychologist, who studies why one does what one does. Learn a bit more about them before you kill them; that way you might prevent yourself from being "wronged" yet again.