Is this really hate speech?

One of the people in my school got detention recently. As a result, after school, he posted on Twitter a bunch of statements to the teacher that reported him and to the principal. He included stuff like vandalizing the principal's home and harming his family. As a result, the school suspended him. He's saying that the suspension is a violation of his freedom of speech and that the statements he made are protected as hate speech. The school, on the other hand, is saying that those statements on Twitter are just creating a clear and present danger to the school and its staff.