On the other hand, wrong. IMO, no one should cause anyone else to die if at all possible.

This actually is indirectly one of my uncomforts with the death penalty. I ultimately support the death sentence intellectually, but carrying it out is a different story. I cannot imagine being the person (or persons) responsible for carrying out the execution of an individual because some other people told me it was the right thing to do.

That's the basis for the wrongness of the original murder.

Not quite. The wrongness of the original murder was that the person knowingly took an innocent person's life and displayed a disregard for that innocent life. ("innocent" meaning non-murdering).

I've yet to see how killing him is going to help matters.

Two answers: Justice and deterrent. I feel that you definitely wouldn't agree with the concept of "Justice" in this case, so I'll leave it alone. As far as being a deterrent, it hardly works now because the system is so messed up. It takes so long to execute a person that there isn't any perceived loss attached to the action which receives a death penalty. Even if it were more immediate, there are still reasonable questions to how much of a deterrent the death penalty would prove to be.

For my own part, I do support the death penalty, but not without reservation. The concept of anyone taking another person's life and that person knowing it's coming and being powerless to stop it because the action is protected under the law does bother me.