The previous answer correctly states the names of the schools that Holden leaves, for one reason or another. At Pencey, his latest school, it seems like he simply didn't apply himself and so he's been kicked out.
However, as a general thing it seems that Holden struggles less with the academic side of things in schools than with the social. He feels like he's surrounded by 'phonies' all the time, both among teachers and among his peers: insincere types, boring types, self-satisfied types, and so on. He attempts to explain his departure from all those schools later to his kid sister Phoebe, although he thinks that maybe she can't understand. However, it is enough that she listens:
But she was listening, at least. If someone at least listens, it's not too bad.
Of course, Holden's complaint about his schools being full of phonies is maybe only a cover for his own inadequacies. He certainly does seem to struggle a good deal with making connections with his peers and authority figures, even taking into account the fact that he is in the throes of adolescence. The only people he seems able to get on with are his own family, at least his siblings: he remembers his dead brother Allie with excessive fondness, and gets on well with his little sister, Phoebe, and also obviously respects his older brother, D.B.