Most of you have serious brain problems, the father explained it really well why she needs to go to the academy and spent almost the whole chapter telling her she has talent, but you guys are forgetting something else, he isn't only her father, he is also the head of the house.
Imagine how other nobles are going to act against a "weak" head of a noble house, he had to exile her to protect her from revenge from people around them (because she lost value after being exiled) and also to get rid of the engagement since she will not be part of that house anymore.