We have bullies in schools because we don’t punish them.
Next question, why don’t we punish them?
Teachers and administrators are scared of the bullies too. Some have guns and can find where you live.
Teachers and administrators don’t want to hassle with it.
Some teachers and administrators are bullies too.
Administrators don’t want to expel bullies because they will lose some funding (though, they’d find out they wouldn’t need to expel many bullies, because many would come into line and they would find more people would want to send their kids to that school).
Administrators don’t want to expel bullies because of threats of lawsuits, the mere hassle of which can cost resources and time.
Administrators don’t want to expel bullies because they believe everyone is entitled to an education, no matter how bad they act. And they believe they can talk it out, rather than enforcing real consequences.