Capital Punishment

The arguments in favour (deterrence; punishment) seem to me unconvincing, but I'm puzzled that the thsoe who oppose this business frame their arguments they way they do. For many, their objection to capital punishment is expressed via the concept of 'but he doesn't deserve it' (maybe he is innocent; maybe nobody deserves such a fate). That's fair enough, I suppose. But what if he does deserve it? That sometimes happens. Harder to counter, it seems to me, is the fact that everybody is situated, socially, familiarly. If a man murders another, he does no further hurt to his victim (who, being dead, is beyond hurt); but he does grievous hurt to his victim's loved ones. Similarly, when the state murders this murderer, even if the criminal deserves it, the criminal's wife and children, his family and friends have certainly done nothing to deserve the terrible pain and bereavement the state inflicts upon them.