What do tap dancing and a half nelson have in common in relation to The Catcher in the Rye?
These two activities are performed by Holden with Stradlater, his roommate. In Chapter Four Stradlater returns to the dorm to shave. He is "a jock" as muscular and handsome young men then were called. As Stradlater goes down the hall with his razor and shaving kit, Holden, wearing his red hunting hat, Stradlater asks Holden to write an essay for him, and because he is "madly in love with himself" he believes others want to do things for him.
Holden finds it ironic that Stradlater asks him to write a composition since he is the one who is flunking out of the school. Holden, who has been sitting on the washbowl next to Stradlater decides to clown around, so he
...backed up a few feet and started doing this tap dance just for the fun of it. I started imitating one of those guys in the movies.
Tap dancing was a popular form of dance in Holden's time; such stars as Fred Astaire, Gene Kelly, and Sammy Davis, Jr. were in movies.
Then, he asks his roommate if his date is a girls with the last name of Fitzgerald. Stradlater let's out an exclamation and says, "Hell, no!" Suddenly, Holden feels comical and wants to fool around, so he tries to put a "half-nelson" on Stradlater. This is a wrestling hold that is effective when the wrestler wants to "pin" his opponent and win. A half-nelson involves putting the arm under the opponent's armpit and locking the hand on the back of the opponent's neck. By pushing on the neck and lifting the shoulder, the opponent can be turned over. But, Holden is not strong enough to gain complete control of Stradlater, so Stradlater breaks his hold, scolding him to stop "horsing around."