I also believe that capital punishment is abhorrent because it is little more than revenge. You killed, so we will kill you. That is a crude rendition of collective social thought, but I think it is a very crude notion. Revenge is the very base of human impulses. It occupies the same rung as all murderous impulses.
Revenge is a reason for murder, like greed and envy are motives for murder.
Revenge is a desire Civilization should distill and refine such impulses so that we can collectively become something better than our instincts. The practice of capital punishment, however, codifies and shrouds in robes of law our desire to be made whole by doing onto other as they did on to us. Recall, capital punishment is a social norm, not the family of the victim exercising their desire for retribution. We as a society declare that a convicted person's life is forfeit for the acts they were convicted of committing. This grand pronouncement bestows on the act a higher purpose.