"I still don't see why murdering murderers is wrong"

Because you are committing the act you are punishing them for. No matter how much you bureaucratize and sterilise it you are still committing murder. A government can not prophess a certain act to be the worst act one can commit, and then punish that act with the same act. It is hypocritical and, well, just plain stupid.

If government and society wants it's citizens to believe that murder is wrong then fair enough, you won't get any objections here. But executing somebody for murder is as ridiculous as a parent who spanks their children for fighting, and tells them that violence is wrong.