Those who support the death penalty want justice, not vengeance. 

Vengeance is exacting more punishment than the crime deserves. Justice is exacting the exact punishment the crime deserves. Mercy is remitting some or all of the punishment the crime deserves. 

A life for a life is just. I am not saying we should never have mercy, but a life for a life (assuming first degree murder--the worst possible crime, etc) is hardly vengeance.

If you think the death penalty is immoral, how can you possibly support abortion? If it is immoral to take the life of a guilty person, why is it moral to take the life of an innocent person?