In my previous post I explained that for political theorist John Locke, there is really only one right - life. All other rights, such as the right to property, flow from that one right. One might be left with the impression that Locke's philosophy would lead one to oppose capital punishment.
Locke held that our basic rights are sacred and cannot be violated. If one were to violate those rights, society had the right to demand dire punishments. But not even the government was allowed to violate the rights of the individual. So how does this work. One important phrase in the Bill of Rights is "due process of law". In other words if it can be established that a certain person has indeed violated the basic rights of others, their own rights can be taken from them. So if a person deliberately takes the life of another, or serious threatens it by deliberate, malicious acts, and this can be publicly established to be the case, their life can be taken.
The real issue is do we consider our basic rights to be so precious and sacred that we will as a society stand up for them? For students of Locke they are. So the death penalty is really the result of seeing individual rights as precious. In fact we view them as so precious that we will require that those who violate the rights of others, forfeit those rights themselves.