And that's it right there. If we put this kid who lost his temper, like a kid, in the adult system we are essentially guaranteeing ourselves that upon his release he'll be useless as a productive member of society and will almost certainly turn to crime and do even more harm to society. Forgetting about the kid for a minute, that's not a good deal for the rest of us.
Let this kid deal with this through the juvenile system. It might be light on destructive vengeance according to some of your tastes, but it provides for the possibility that this kid won't turn into an adult who's only contribution to society is more crime and violence.
It all depends on how he is now. If he is already lost then there is very little we can do for him.
If it truly was a decent kid who lost his cool then I agree adult jail time makes no sense.
If I'm the judge I find out more about this kid. What kind of student is he. What do his peers say about him.
If he is a problem child that has a record of causing problems then it's already too late.