Holden Caulfield is an intelligent but insecure high-school junior who is expelled from Pencey Prep which is the fourth boarding school he has attended for failing four out of five subjects. Although Holden seems likable and has a good sense of humour, he has difficulty facing reality, in particular his inability to adjust to his peers and society in general.
Caulfield is immature and refuses to grow and doesn’t like to moved on. He wears the red hunting hat is certainly a peculiarity at Pencey Prep and in New York City. And that is precisely what Holden himself wants to be, different and unique. In short, the hat is his red badge of individuality. Holden's hat could also symbolize his own personal hunting expedition for himself. Further, its colour could symbolize his dead brother, Allie, who had red hair.
Holden's ten-year-old sister, the only person with whom he can communicate while feeling completely at ease . He loves and admires her, and she seems destined for success in all of her work because of her precocity. However, Phoebe exhibits some of the qualities of Holden. For example, she writes books about a girl detective but never finishes them. Her failure to complete them parallels Holden's failure to complete school. Moreover, when Holden decides to run away, Phoebe impulsively follows him and insists that he allow her to accompany him.
Phoebe is probably the very opposite of Holden. She is mature for her age and gets good grades in school. This is why Holden admires her.