This is a good question. It is probably good to start with the observation that Holden does not like school at all. It is true that he does not like Pency, but he has gotten kicked out of four other schools before this one. In light of this, it is safe to assume that school is not for him.
Second, it is pretty clear that Holden is not a good student. At the beginning of the book, he is notified that he will be expelled from school due to his failing marks. He just failed four courses. This is not to say that Holden is unintelligent, but that he has no inclination or desire for academic book study.
Third, Holden does not like his classmates such as Stradlater. One of the most commonly used words is "phony." Holden sees the phoniness of al the people around him. He is pretty insightful. Ironically, he does not see this in himself.
Finally, Holden is at a juncture in his life, where he is filled with rebellion. For this reason, he does not like school in particular and authority in general.