Everyone is single.
In school, characters who may not want to deal with each other socially are forced to deal with each other. If someone was being bullied by Sarah in an adult story, they'd just walk away--what's Sarah going to do, after all?
Characters are living at home, so have parents and siblings who can get involved, without it being negligence. (If Zoe overhears Jon and takes the stone, that's fine. If a child takes the stone from a parent, that's irresponsible parenting and the equivalent of leaving a bottle of drain cleanser around and having your five year old drink it).
Like classmates, parents and siblings are people who you are forced to deal with.
It's more plausible to have a "characters dealing with their sexuality" plot.
Kids often have more free time than adults.
Kids can do immature things and it makes more sense. I'd never expect an adult character to turn himself into a character from a video game, despite the fact that many adults play video games.
School is universal, so more writers know about it than about any specific setting past college.
Which is not to say that you can't do some similar things with adults, but the possibilities are more limited.
