I see where you are coming from, and even admire it in a way, but I feel compelled to point out another side of the issue (one other side, there are probably 20 more). Online bullys don't usually just make speech involving insults and putdowns. There's a high degree of these being accompanied by false accusations that can easily count as libel, and by misinformation which is often damaging in other ways. (In fact, for cases where bullying goes on for over 3 months, the chance of one or more of these other actions approaches unity). We've seen cases where, for example, the bully has progressed to claiming that a victim is HIV+, and then giving out a lot of misinformation about HIV in general, falsely claiming to be a doctor or to have gotten the information from one, an/or claiming to having hacked their victim's medical information. These things are generally criminal in and of themselves, and/or have other negative impacts (such as triggering security audits of medical records keeping to make sure the bully's claim isn't genuine), Protecting teens against insults and put downs is a mixed bag, but when you add in protecting them from bad medical and legal advice, and false claims that they can't protect their records if they see a doctor, and so many other things, any sane society is going to opt for some limitations, at least with regard to minors.
This form of bullying has many interrelated bad effects: Laws get passed, because existing laws don't seem to be stopping the problem behavior. Free speech becomes hard to protect when the test cases are such unsympathetic types - even the ACLU sometimes declines to take a case where the jury is likely to be looking for any chance to convict on anything remotely applicable. Even if a politician actually cares about free speech (I know, I know, but some of them actually do.). The ones that actually try to live up to the Constitution, the UN declaration of rights, or other such inspirational ideas are also the ones who really want to stop these other related abuses, so even they will look to compromise (and for the ones who are just pandering to whatever group will get them elected, that sort of compromise is a no-brainer). Let a creep get away with enough, and everybody wants to see some sort of blowback, and if it looks like that creep is just hiding behind a first amendment claim, then the first amendment starts to be called a "technicality".It takes more character than most have to defend Vlad Adolph McKnife-wielding-Psycho. That's why there are phrases such as "Online Stalker" - behavior analogous to real world stalking, not just insults.
My feeling is, even if we should let kids naturally develop tougher skins and reognize that free speech includes just the sorts of speech we find ourselves half wishing there was a law against, there's too many real creeps on the net for it to happen. The best way to stop it would be for the laws against slander, libel, and impersonation to be enforced so the things that are not just speech are what we are regulating, but we don't seem to do that, so bad laws WILL get passed instead.