The Catcher in the Rye by J. D. Salinger is an iconic study in adolescent rebellion, with the narrator, Holden Caulfield, often cited as an exemplar of teenage angst.
Before the story begins, Holden has just been expelled from his third prep school. This itself is a sign of rebellion, as expensive prep schools rarely expel their wealthy young pupils. Moreover, his failure in his classes is not due to lack of intellectual ability or preparation, as he is an intelligent young man whose father is a successful lawyer, and his mother, although suffering from the loss of Allie to leukemia, is a traditional concerned upper-middle-class parent. Holden's bad performance in school is not due to a bad family environment or extreme poverty, but instead to his own refusal to do schoolwork that he doesn't like; this is key evidence of his rebellious nature.
His trip to New York, in which he roams the city rather than return home, is also a gesture of rebellion, as is his flouting of many conventions both mentally and in terms of his actions. His condemnations of the entire world around him as "phony" is a key element in his rebellion, as it legitimizes his refusal to accept adult authority. His indulgence in alcohol and the scene with the prostitute are also acts of rebellion.
The account that Holden gives us of himself contains many different examples that show he is a rebellious personality, so much so, in fact, that the name Holden Caulfield has become almost synonymous with teenage rebellion and a determination to live one's life outside of the expectation and demands of society. Let us consider one of the first examples we are given in the book, where Holden tells us, almost as an afterthought, that he is being expelled from Pencey, the incredibly elite school where he is studying:
I forgot to tell you about that. 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 and all.
As the narrative continues, we realise that this is not the only school that Holden has been expelled from. His rebellious personality is thus indicated through the way that he obviously refuses or is unable to bow to the demands of society and work hard at school to gain academic success. You also might like to think about the way that he sets off on his own personal odyssey doing what he wants to do and his frequent, romantic and impractical, plans to run away and live away from the norms of society.