In The Catcher in the Rye, Holden Caulfield is looking for a community in which he feels welcome. He has not found this at Pencey Prep—especially not in his roommate, Stradlater. Back home, now that his brother is dead, he only feels close to his sister; their parents are distant and his mother seems trapped in her grief.

Holden knows that Stradlater is an opportunistic bully. He expects Holden to help him cheat at his school work, and, when Holden caves to the pressure to do so, he objects to the way Holden complied with the letter but not the spirit of his coercion. Holden understands that Stradlater is an unprincipled egotist and he does not respect him. He calls him "unscrupulous," says "He was mad about himself," and repeatedly calls him a "moron." Holden believes that insensitive people like Stradlater have it easy because their conscience does not bother them.

These feelings as well as his roommate's possible sexual relationship with Jane combine to cause Holden to lose his temper and respond to Stradlater’s light punches by trying to hit him hard.

I'm not entirely sure that it does show this.

To me, that fight is a better example of the fact that Holden will go out of his way to argue with anyone. In this case, Holden actually pushes things too far, and gets physically beaten as a result. I think that beating was something that Stradlater would have just as well avoided, but Holden kept on about it.

Holden does say that he likes Stradlater, and in some ways, he demonstrates that he is jealous of Stradlater, so I think he does like and respect him...but I don't know that he is looking for that, per se. 

Dave Becker