The death penalty is wrong and problematic on many levels, but the simplest is;

It is wrong because two wrongs don't make a right. Why is it called "murder" if an individual kills someone, and "justice" if the State kills them? Either is a murder, and neither is ethically sound. I will agree that some perpetrators have committed horrible acts and show no remorse - that doesn't give the State the right to be just as bloodthirsty. There are other, more ethical ways to punish offenders.

Humanity is supposed to be trying to move toward a less barbaric condition - one sure way to do that is to abolish the death penalty, world wide.