Why is Holden expelled from Pency? What are his reasons for disliking school?

Holden's views of Pency Prep are as stark and absolute as his opinions on so many things. He makes no defense for himself, however, when he announces why he is being expelled. 

"They kicked me out. I wasn't supposed to come back after Christmas vacation, on account of I was flunking four subjects and not applying myself at all."

Holden first mentions Pency very early in the text by referring to the advertisements that the hypothetical reader may be familiar with because they "advertise in about a thousand magazines." These ads show Pency Prep as a place where "some hot-shot guy on a horse jumping over a fence" is coupled with a catch-phrase ("'Since 1888 we have been molding boys into splendid, clear-thinking young men.'"). 

In Holden's view, Pency does not "do any damn more molding" than other schools do and the advertisement is thus a false one. This perspective on Pency as a place that presents itself under false pretenses is significant in light of Holden's predilection for pointing out how phony so many things are and also in light of Holden's own narrative, wherein he presents himself in a certain way that leaves quite a bit out, as he admits in the opening paragraph of the novel. 

The notion of presentation versus reality relates also the the idea that the truth lies under the surface and must be experienced to be understood. We might take this conceptual ethos as one of the driving themes of the novel as Holden recounts his difficult period (and nervous breakdown) not as an explanation of a state of mind but rather as a narrative that the reader also "lives though" and experiences.

There is no ultimate denouement or revelation of the mechanisms of Holden's anguish (not even a direct statement that he is essentially working through his grief over the loss of his younger brother, Allie). Instead the story remains somewhat evasive and oblique. This character of the story means that Holden's self-presentation is subject to some of the same scrutiny that Pency Prep is subject to. If Holden despises Pency as a phony institution because it does not live up to its own self-promotion/self-presentation, we might wonder if the same incisive observations are invited into Holden's character and his story. 

Holden's relationship to Pency is important in the ways that it demonstrates his general social demeanor (aloof, antagonistic, disgruntled, etc.) and his inability or unwillingness to engage with anything associated with the future. Holden's apparently self-destructive tendencies are part of what leads him to be kicked out of the school and they continue to drive his behavior throughout the story.

Yet, Holden's acceptance of his own role in the expulsion is an important indicator of his ultimate honesty. He may be mad at the world, but he is also indicted by his own point of view. This makes Holden complex as a narrator and as a character and, on another level, suggests that he has the potential to mature into an honest world-view.