Holden Caulfield is more a typical teenager than a rebel. But he is a typical teenager dealing with a deep depression and disatisfaction with life. Considering that Holden begins telling us his story from a mental institution, it is clear that there is more than teenage rebellion going on in his life.
His repeated failures in school are not typical, common, maybe. It is, however, for Holden, symptomatic of a larger issue. I believe it is his inability to deal directly with the death of his brother. He feels isolated from the world, he makes no meaningful connections at any of his schools. He really has no friends. His closest relationship is with his 10 year old sister, Phoebe.
Holden is an outsider, he cannot engage in the normal activities of teenagers with any joy, because he finds fault with the world he lives in, everything is pointless, or without value. Holden rejects the world that allowed his younger brother, Allie to die at 14. He finds fault with the schools he attends, he finds fault with the students at Pencey Prep, school is pointless. The only time he has any fun is when is pretending to be someone else. As when he meets a parent on the train going to New York and uses a fake name and lies to the woman about her son. But then he feels more lonely. He is a complex character.
Holden's problems are deeper than the usual teenage rebellion. His behavior is unstable clearly indicating a degree of mental illness.