DSM-V doesn't have anything listed for "recipient of mean words"
That's quite surprising, considering the amount of fluff included in the latest version. Don't worry though, chances of something like that being included in a future revision are quite high. (snark is good against depression - see what i did here? regardless, please do keep in mind that it's not polite to bring DSM-V into a serious conversation. if it really must be done, use an earlier version)
It's not easy. Nothing in life ever is. But it's worth it... and you have something I didn't -- a mother that cares. Lean on her until you can stand up straight again. [*] You're a survivor. You can do this.
(* Skipping irrelevant bits)
Hmm. I would be quite tempted to hit you with some more snark for this part, but that would be ill played considering the rest of that paragraph. Still, you might want to consider your own earlier words:
People will tell you that you have to try harder, or just "will" yourself to be happy. You and I both know that's stupid
so simply saying You're a survivor. You can do this. is ... well, you get the idea. Any depressive that's not on medication will ask you a simple question: why? and demolish that argument. If you truly want to write that kind of letter and not just bandy words on /. consider the problem of choice - the lack of it, specifically. Depressives often enough have one way of coping with a situation, and it's a way that is (shall we say) inadequate; hence, the lack of alternatives is a big part of the problem. And depression is not exactly the most find-other-ways-enabling state of mind. I would humbly suggest, as an alternative approach, showing (not talking about) alternatives, even for minor things. To paraphrase a dead French pilot who wrote about little princes, I can describe for you the view from a mountaintop and you'll never have an image for it if you never saw it, but if I bring you there, you'll see it and you'll have your own image. The best thing imho that one can do for a depressive is enable choices. And if, given several choices, suicide still follows, then maybe a life had to come to its end, and these things can happen if you place any value on freedom of choice. But sadly it sounds as if this boy had none.
Ah, and one more thing. I would submit that it's not exactly the brain trying to kill anyone here. Brain cells and their activity suffer quite a bit in a depressive, and I'd count the brain as a victim as well. But that's just a personal opinion.