We actually use both in school and at school, for slightly different situations.
At school means the person is literally, physically, inside the school.
(conversation at 2:00 PM)
“He’s at school. His classes finish at 3:30.”
In school means the person is studying in general (usually at college or university) but not necessarily inside the school building at that moment.
“My husband doesn’t have a job because he’s in school. He’s studying law.”
I can say this sentence even if my husband is not at the school at that moment.