Why is that? Can you show me one other business that should have to continue to deal with a customer who publicly smears them on social media, lest they suffer the opprobrium of being "a-holes" in the eyes of people like yourself?
And there may be some question as to whether they can take payment for service then deny service, although I assume that sort of thing is covered in the small print someplace.
Prorate and refund her money. Problem solved. Let her go find some other school to be an idiot about.
Did I not say they are entitled to part ways? From the sounds of it the school messed up and then tossed this customer out over a pretty minor "smear." Can they? Yes. Should they? Thats down to opinion, and tempered by my own dealings with schools both private and public, I generally find that school-people are usually both ignorant AND A-holes, which inclines me to say that the school is overreacting.