How did Holden become a good writer?

J. D. Salinger wanted to use a sixteen-year-old boy as a persona and as the narrator of his novel, but Salinger was concerned about verisimilitude. How could Holden Caulfield, a boy who has flunked out of three of the best prep schools and has therefore had virtually no high school education, narrate a novel as perceptive as The Catcher in the Rye? Salinger has two different persons compliment Holden on his writing ability. One is his roommate, Stradlater. When he cons Holden into writing a descriptive composition for him,
"Just don't do it too good, is all," he said. "That sonuvabitch Hartzell thinks you're a hot-shot in English, and he knows you're my roommate. So I mean don't stick all the commas and stuff in the right place."
Holden may use a lot of slang and profanity in the novel, but we can see from reading The Catcher in the Rye that he has all the "commas and stuff" in the right places.
The other person who compliments Holden on his writing is Mr. Antolini, his former English teacher at Elkton Hills. Mr. Antolini wants to know why Holden got expelled from Pencey Prep.
"What was the trouble?" Mr. Antolini asked me. "How'd you do in English? I'll show you the door in short order if you flunked English, you little ace composition writer."
A large part of Holden's writing ability is attributable to his keen interest in reading. He is an autodidact. In Chapter 3 he tells us:
I'm quite illiterate, but I read a lot.
This probably means that he reads what he feels like reading but has failed to read a lot of the books he was supposed to read, including the textbook for Mr. Spencer's class, of which Holden says, "Well, I sort of glanced through it a couple of times."
Holden tells us:
I read a lot of classical books, like The Return of the Native and all, and I like them, and I read a lot of war books and mysteries and all, but they don't knock me out too much.
He mentions The Return of the Native by Thomas Hardy, Of Human Bondage by Somerset Maugham, and Out of Africa by Isak Dinesen, as well a collection of short pieces by Ring Lardner. We can see that he must be intelligent and discriminating as well as eclectic in his tastes. This explains why he has become a good writer although he has such a deplorable academic record. The Return of the Native, Of Human Bondage, and Out of Africa are heavy reading for a sixteen-year-old who flunks out of his third school for scholastic ineptitude. Here is a boy who gets A's in English and F's in everything else. We easily get hooked on The Catcher in the Rye and are easily able to believe it was written by a sixteen-year-old boy just like Holden Caulfield.