I’ve found this over the years. Every time someone talking to me mentions capital punishment, I don’t have much to say. In a way, arguing about capital punishment is like arguing about religion: there is no point. You can’t prove, you can’t persuade.
So every time I just end up mentioning a story I’ve once read. Young Amis and Hitchens are telling Saul Bellow about the sheer absurdity of taking away a life you haven’t created. The immorality of that. The senselessness. And Saul Bellow, being the great man that he was, throws this as a way of reply (quoting from memory, so I might be slightly off): “Yes, but what do you do with that son of a bitch who raped and murdered his own daughter?..”
For me, any sensible conversation ceases after that. I’m not a Western man. I trust emotions, rational thinking has never done much for me.