Catcher in the Rye's is open-ended. Salinger gives provides an authorial voice at the end (Mr. Antollini), but he doesn't save Holden. So, in the end, the reader can make either case: Holden does mature and Holden does not mature. It's an anti-climatic ending full of regret as Holden says that he misses everyone. By the end, the reader is back where s/he started.
Here's what Enotes says about the ending:
Chapter 26 functions as an epilogue to the book. It is outside the story. Epilogues usually help explain what went before, but Salinger leaves this analysis to the reader. Whether Holden ended up as a Wall Street attorney, working at his father’s firm, or is, in fact, still frequenting Central Park, cursing the absurdities of life, nobody knows. Maybe Salinger knows, but he has said nothing—in over 40 years.
Here are my lecture notes (with quotes) regarding the final chapters:
I. No Deux ex Machina
A. literally “God out of the machine”
B. literary definition: “a plot device or character that rescues a hopeless situation”
C. Mr. Antollini: voice of Salinger; Mr. counter-culture professional
D. has a chance to rescue Holden
E. His advice:
1. Holden is “in for a terrible fall”
2. "The mark of the immature man is that he wants to die nobly for a cause, while the mark of the mature man is that he wants to live humbly for one."
F. Salinger discredits Antolini in the end by casting him as possible gay pedophile (no rescuing; no morals)
G. Anticlimactic ending: does Holden ever grow up? "don't ever tell anybody anything. If you do, you start missing everybody" (shows regret; a downer)