This is not a question of punishment. I don’t believe in punishment. Who are we to judge? In this sense I agree with popa that we have no idea why the kid is like this.
But I don’t think locking up a murderer or executing him is about punishment either. It is about protecting society from him, and it’s about making other potential criminals think twice.
Does this kid deserve to be maligned? It isn’t relevant. The community is more important than him. If he hadn’t done anything then it might not be morally right to make such a judgement call of individual versus community, but he jumped on the scale by committing his crime.
Can he do teshuva? Of course! Is it possible that he isn’t even at fault for his actions, due to some deeply rooted issue in his brain caused by someone else? Certainly. But that makes no difference to us, as a functioning society. If someone’s bad upbringing were causing him to come at me with a gun, I’d still run him over with my car. His personal motivations are between him and God.
Once you jump into the ring, my life comes first. Otherwise society goes down the tubes.