How does Holden experience coming of age, that is, how does he mature from the beginning of the book to the end?

One could argue that we know Holden has matured when he returns home, instead of running away. Near the end of the novel, Holden decides that he needs to go west; he even writes Phoebe a note to meet him, so that he can say goodbye to her. When Phoebe arrives with her bags with the intention of joining him on the trek, Holden changes his mind, however. He seems to change his mind because he realizes that his little sister cannot run away from home, not because he should not. Nonetheless, "Going home seems to symbolize rebirth, getting his life in order, maturity."

In the final chapter, the reader understands that Holden has been telling his story from a mental institution. We can take whatever we like from that-- Salinger has certainly left all meanings wide open. But one could argue that with maturity comes self-reflection. Maybe Holden realized that he needed help.