To be honest, it is an oddity of English. And, sometimes, we do say "in school" or "at the hospital". A difference can be when a person is engaged in the services of those places, they are "in" them. If we talk of the person's location only, we say they are "at" them. When my son goes to the hospital for blood tests, I would describe him as "at the hospital". But when he stayed overnight because of an illness, I would say he was "in the hospital". If I was describing where my daughter was in the morning, I would say she was "at school". If I was describing why she was not home, I would say it was because she was a student or that she was "in school".