Holden desperately needs to relate to people / empathise with them. He wants to see what somebody has written as an expression of their personality. You can see their personality from the ideas expressed in their composition, but not its use of commas. Therefore he's not interested in punctuation as the above quote shows.
When Holden says Stradlater 'wanted you to think that the only reason he was lousy at writing compositions was because he stuck all the commas in the wrong place' , it suggests that Holden thinks the real reason is Stradlater lacks sufficient inspiration for his compositions. Holden thinks Stradlater is a shallow person, and one he finds difficult to relate to.
It is true also that Holden is a rebel and doesn't abide by the rules; his lack of concern for the rules of punctuation is just one example of this. So this passage in the book shows Holden's need to empathise with people and his disregard of the rules.
Salinger evidently wanted to write an entire novel in which a sixteen-year-old renegade boy writes a criticism of his society as he perceives it. Many of Holden Caulfield's observations are quite sophisticated because, after all, the novel is being written by Salinger, a much older and more experienced man. Salinger took some pains to establish that his young hero, in spite of his poor performance at some schools, happened to be a gifted writer, which would hopefully explain his intelligent and sensitive observations and remarks. Salinger also took pains to establish that Holden looked older than sixteen because of some illness that had made him a little white around his temples. This appearance of being older than he really was enabled the hero to go into places where sixteen-year-olds would be rejected. He also needed to look older to check into hotels. Salinger arranged this because he himself wanted to be able to comment about such places as New York nightclubs and also to give Holden more freedom of movement in the big city.The Catcher in the Ryehas often been compared to Mark Twain'sHuckleberry Finn, but Huck Finn was just a kid while Holden had to pass for a young adult because of the urban setting he was exploring. When Holden starts complaining about punctuation, Salinger is creating the impression that Holden is gifted, original and sincere but still just a kid whose understanding of rules of grammar is limited. Less is more. If Holden's grammar and punctuation were more perfect, it would detract from verisimilitude, making it seem that an older author had either written the novel or done considerable editing and revision.