Whoever believes that forgiveness is an absolute virtue is sadly mistaken. Rational self-interest is the only absolute virtue. Forgiveness is only rational if it qualifies as self-interest; i.e. forgiving a friend for getting drunk at your party to benefit the greater interest of your friendship. Forgiving a murderer is an invitation to murder. "Forgiveness" is why 80% of crimes are committed by 20% of criminals.
Put another way, nonviolent conflict resolution works great if everyone is on the same team (i.e. a marital conflict) and is completely dysfunctional when applied to people who are, for lack of a better word, your enemies (serial killers, ruthless dictators, etc.).
The less willing society is to defend itself, the more easily it is abused -- and, paradoxically, the more violent it becomes. How we deal with violent criminals does indeed reflect on us as a people, a society, and a civilization, particularly to those weighing the consequences of pursuing a life of violent crime in that society.
There is a branch of science called "game theory" that models human behavior with amazing accuracy. While too complex to get into here (Footnote 1), capital punishment represents a disincentive for defection that shoots right off the scale. The predictable result, iteration after iteration, is a lot less defection.
Lastly, if we are not qualified to pass moral judgment on others, we need not pass moral judgment on ourselves. We are justified by this logic to kill murderers reflexively, in preventative self-defense, ignoring any moral implications. One need not pass moral judgment on murderers to perceive them as a threat and kill them that way, like a bear kills to protect its cubs. Because capital punishment is perfectly reasonable the only reasonable objection is that it is immoral; ergo beyond the scope of human reason. If, however, no one is qualified to judge morality then who can authoritatively say it is immoral to kill murderers? Meanwhile, morality notwithstanding it is reasonable to respond to a threat, so in the absence of a compelling moral reason not to kill, killing is appropriate. (Footnote 2)
My point is that capital punishment is not only the "right" thing to do, as you so viscerally pointed out, it is also the "smart" thing to do. Do not be so quick to surrender the high ground when you have the advantage of being correct. Sun Tzu said that to achieve victory you must master both the normal and the special forces, and that you must know when they trade places. I do not now know whether the intellectual approach is Cheng or Ch'i, but I do know, whichever it is, you don't just give it up.
Footnote 1: A layman's explanation of game theory might include the phrase, "Fool me once, shame on you. Fool me twice, shame on me." Although crudely put it is the second unifying principle of game theory.
Footnote 2: Because I believe in an absolute morality (based, ironically enough, on cultural relativism) this is not the reason I support capital punishment; nonetheless it is quite an eye-opener for moral relativists. (Moral relativism is, ironically enough, incompatible with cultural relativism! But that is a completely different topic ...)
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