Private schools don’t want to kick out students if they can avoid it, because of the tuition dollars, but they can. And just the fact that they can gives them a lot of leverage, even if they usually don’t.
And there’s also the factor that if Timmy ( or Timmy’s parents ) comes back next year, maybe Tommy and Billy’s parents find another school that doesn’t tolerate whatever it is that Timmy does. Maybe you let Tommy and Billy leave if their parents just don’t like Timmy for some reason - but maybe Timmy is disruptive or a bit of a bully.
I’d hope the school has a waiting list as an indication of the esteem it is held by the relevant community. If so, then “don’t come back next year” is the simplest option unless the situation deteriorates dramatically. I suppose too in the USA, lawsuits are a consideration - it can be expensive if some parent wants to go kamikaze on the school’s legal budget. However, I assume the more presitgious schools have access the top end lawyers as a favour because their children go there.
We had a problem with a middle school Math teacher for FtGKid2.
She was dumb. He is smart. He kept finding mistakes she made. So she decided to make his life hell. We went up the chain and nothing happened.
Eventually we collected enough of his assignment/tests that she gave him F’s on despite the work being correct. And with that he got moved and the teacher was eventually sent elsewhere (no doubt to pick on other kids).
But it was surprisingly hard. It required documentation over several weeks.
Another factor preventing students from being kicked out, even if there’s a waiting list ready to replace them with another tuition-paying students, is that teachers and school officials are human, and therefore don’t like admitting defeat. When you kick a kid out of a school, you’re saying that you give up on them, that you can’t fix the problem. But teachers are always telling ourselves that we can fix the problem, if we just try hard enough. Sometimes, we can, and often enough (I think) that that attitude is a good one to have. But it can also lead to us fooling ourselves into thinking we can still solve a problem even when we genuinely can’t.