I guess a lot has to do with how you interpret "an eye for an eye."

My view: If you take a life, you need to return a life. Taking yours doesn't balance the scale.

To me, the "eye for an eye" justice is to incarcerate the felon who now becomes a medical donor - blood, bone marrow, organs, et cetera - until the scale is considered balanced again by whatever formula one wants to apply. In this way, the felon now has a means to "return life." To kill the felon only rids you of the felon, but the scale is still askew.

Capital punishment is enforced by society, as crimes are harms against society. That's the way our legal system works. If society believes justice is served by killing the felon, that's society's choice until legislation is effected or the judicial system counters its use on constitutional grounds. We have a lot of "societies" here (Federal, State, Tribal and Territorial jurisdictions), all who have wrestled with this issue and are applying in in different ways.

Ironically, the victim (or surviving relatives) has little input on what actually happens to the felon. Again, the "crime" is against society, not the individual. If the individual (or surviving relatives) want private justice, that's a civil law issue for harm/damages due to the commission of a "tort." Remember OJ - acquitted in criminal court, but the loser in a tort claim in civil court for essentially the same action.