Stradlater borrows Holden's jacket to wear while he's on a date with Jane Gallagher, a girl that Holden is enamored by. This shows Stradlater's complete self-absorption. Holden has been expelled from Pencey but instead of supporting his roommate, Stradlater is thinking only of himself and his date with Jane. It drives Holden crazy thinking about Stradlater "giving the time" to Jane.
This is further emphasized when Stradlater asks Holden to write his composition for him. He takes advantage of Holden's sensitivity by pressuring him into doing his homework while he goes on a date with Jane. And when Holden writes the descriptive essay about Allie's baseball glove instead of the room that Stradlater ordered, he is annoyed that the essay is too good and completely unaware of Holden's grief.
Stradlater's borrowing of the jacket is just one example of egotistic personality and insensitivity to his roommate.
When Stradlater borrows Holden's jacket in chapter 4, this shows Holden's inability to say no to people; his inability to go after what he wants; and it symbolizes that even though Holden won't be on the date with Jane Gallagher, but his roommate will, his thoughts will also be as present as his jacket is.
First, Holden can't say no to Stradlater for a few reasons: he looks up to the guy; he's his roommate; he is also more of an alpha to Holden, and Holden would be afraid to say no. This shows how much of a coward Holden is in life; so much so, that he suffers because of his cowardice many times. Next, Holden wants to go down and talk to Jane, but he says, "I'm not in the mood right now" (33). This shows that Holden is a great one for making excuses in life. It also means he misses out on a lot of life.
Finally, Stradlater wearing Holden's jacket while on a date with Jane is like the ultimate kick in the face. Holden could have avoided that, but he allows it to happen because he can't say no and he's a coward. As a result, he can't stop thinking about what Jane and Stradlater are doing together, which torments him and causes him a lot of anxiety.