The best comment I heard was by a police officer who said that in his opinion there are two justifications of capital punishment.
1. It does NOT deter anyone from committing a murder and is not a deterrent in that regards. However, it is a deterrent to that person ever committing murder again. People are murdered in prison by murderers.
2. Our society demands a person not take law into their own hands, to instead allow society to undertake just punishment. Therefore, society should do so.
I just heard last week that a person who had murdered 7 people was being released on parole. How is that justice? Society didn't do its task.
If an individual can kill another person in self defense or defense of another, so then should the government.
I don't think "murder" is the trigger for capital punishment. Rather, it is the level of brutality and the lack of humanity the criminal exhibited. A person robbing a store in a panic shooting the clerk is terrible. But it is not as terrible as the man who raped a woman in the desert and then chopped off her arms with an ax - though she lived. The latter one is more deserving of death and the more a future danger to everyone. The death penalty should be reserved for mad dogs who found pleasure in extreme violent and multilating acts of sadism.
I also believe in banishment.