"Does "punishment" exist? That's a rather religious question, because in order for punishment for exist, you'll have to believe in some cosmic authority"
Not true. Why do I need a cosmic authority? All we need to use is common sense. Does it feel good to be punched in the face? No, it doesn't. So, we can safely say that (Though subjective, it's the best logical route of understand "bad" and "good") someone punching someone in the face when that person does not deserve it is "wrong". That person has done "bad", so why not be punished for it, and if so, why not be punished with something that is as severe as what they're being punished for?
If we need a divine being to have punishment, then why do we have prisons? Why should I be punished if I decided to kill someone's entire family? I shouldn't. Morals are purely subjective, but that does not mean that one moral can't be less logical than the next, and therefore we should base our "rights" and "wrongs" on logic and reasoning. I would say popularity, the the majority of the world are fuckin' idiots and Christians.
"and also the totally bananas notion that two "wrongs" makes one "right""
But how would it be two wrongs? Say that it's established(I say it should be) that someone being punished with something as severe as the "wrong" they have committed is the "right" thing to do? Therefore there are no two wrongs.
"You just want to hurt people without taking the blame for it"
Isn't that the picture you're painting for these three boys? They won't to hurt this man without having to take blame for it?
"You want to prevent deaths or more harm? No. If you really wanted to prevent deaths and more harm, you'd be more along the line of isolating them from the world, like putting them in a padded cell, and giving them help and therapy. If all goes well, then within a few months you'd have a couple of socially functioning citizens again."
You could never trust someone who committed such a crime in society. And if you were to "help them" and release them into the world, you would be taking a huge chance, and putting other's lives at risks for this "test"(To see if they will act accordingly). If you are a person who is willing to take innocent lives for unfounded reasons, why should you not deserve to be killed?
I mean really, your entire arguement seems to me that you see no difference in someone killing a kid, and someone killing Hitler. No amount of pseudo-logic will get you around that.