Our society does not truly condone or express interest in the Old Testament eye for an eye type of justice - we do not support the removal of limbs or torture, we do not force the criminal to forfeit their property (other than money) as direct restitution (criminal law does not generally include a commitment to the victim other than jail time - money is doled out in civil court), nor do we support the killing of the perpetrator's family in the case of murder. Rather, our support for capital punishment comes from something less direct and more limited in scope - the idea that there is a point at which a criminal act goes too far, crosses a line that there is no returning from. Some crimes, to a particular society, are so heinous, so unforgivable, that allowing the perpetrator to live, even in jail, is an affront to the victim(s) and to society (Cohen, 19). Our communal outrage will not let us suffer the criminal to live. When that point is reached, the death penalty is the only response we can give. No one is foolish enough to believe that killing a killer will bring back the victims of murder....

But the need for revenge, the need for justice, is exceptionally strong. In other times, in other countries, personal revenge would have taken the form of what we would now refer to as vigilantism. Without knowing that the death penalty is there, that it can be applied to the killer of your children, how would you act? The truth is that we can't adequately answer that question. For many, though, the answer would be direct and equal retribution - kill the killer. but, that would simply make the victim the victimizer, that person would then be responsible for the taking of a life. No, it is better, then, for the state to take that burden away from the victim and the victim's family and community (Coope, 21). The Death Penalty allows for the punishment of particular crimes to be handled on an impersonal nature - institutionalizing death, in the very limited number of cases in which it is used - creates a context that takes the decision to take revenge, to become a murderer yourself away from you and relieves you of it.
We have to understand that the death penalty is used only a fractional percentage of the time - even when justified and potentially used, it is not always so. Because of this, the death penalty becomes less about a specific punishment metered out on a regular basis like a traffic ticket, but a well thought out process that examines the extent of the crime and whether or not the community and victims would be best served through the killing of the criminal. States have exercised their right to opt out of death penalty statutes, but the majority continue to support them and use that punishment - so that citizens may feel protected by the state. The death penalty serves a direct purpose, and as such, it succeeds in providing justice where the individual can't or shouldn't.