How does Holden experience coming of age, that is, how does he mature from the beginning of the book to the end?
Throughout the novel, Holden fears growing up and has a mental breakdown as he transitions to adulthood. He does not want other children to experience the "phoniness" of the world and become corrupted by society. In a conversation with Phoebe, Holden mentions that he wants to be a catcher in the rye, and save children from falling off the cliff. Being a catcher in the rye is a metaphor that represents Holden's dream of saving children from entering the disillusioned world of adults.
Towards the end of the novel, Holden meets up with Phoebe, who plans on traveling West with her brother. Holden initially upsets Phoebe by telling her that she cannot accompany him, which makes her cry. Holden then tells Phoebe that he changed his mind and has decided to stay home. Holden and Phoebe then go to the zoo, where Phoebe insists on riding the carousel. Holden watches from a bench as Phoebe and the other children riding the carousel attempt to reach for the golden ring. Holden fears that the children will fall off their horses, but doesn't say anything. Holden says:
The thing with kids is, if they want to grab the gold ring, you have to let them do it, and not say anything. If they fall off they fall off, but it's bad if you say anything to them.
Falling off the horses on the carousel parallels the children running off the cliffs in Holden's earlier comments regarding what he wants to be when he grows up. Holden's admission that he has to let the children attempt to grab the gold ring without intervening is analogous to him allowing children to run off cliffs, which metaphorically means that he is willing to allow children to enter the world of adulthood without stopping them. This is a drastically different perception from Holden's earlier views of saving children from entering adulthood. Holden's different outlook concerning children entering adulthood illustrates his maturation throughout the novel. Essentially, Holden accepts the fact that there is nothing he can do that will prevent him, or any other children, from eventually becoming adults.
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.