Exposing a bully does exactly that.
If all it were was exposing them, I'd agree with you. If all he got from the internet was dirty looks wherever he went, that would be fine. If something good came from it, like an arrest and conviction, that would be an acceptable resolution.
But you know it won't stop there. This guy will receive death threats, people showing up at his home, his job, etc. And it will affect not only him. The people he lives with...maybe family, children...will also become the victims of the retaliatory bullies from the internet. And if they live in a multi-family home, other people that live there, who have nothing to do with what happened, will also become victims, when something like a brick intended for the bully's window misses and hits theirs.
He was one bully, bullying one girl. And yes, it ended badly, but he will be not just bullied, but terrorized by the internet, lots and lots of people behaving badly, thinking that the wrongs they commit will make it right.
Exposing him says bullying is wrong. Encouraging people to bully him by giving out his address is saying bullying is ok. It says that vigilante justice is a good thing. You make him the victim of an internet lynch mob who will show up with the equivalent of torches and pitchforks. And I can't support that.
and two wrongs never make a right.
Nope. But three lefts do!
I had a feeling someone was going to say that.