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.