Holden is the manager of the fencing team, I'm not sure why he has this position, but from reading other works about fancy Prep school settings, it is possible that Holden had to either play a sport or be part of the staff that supports a sport as a requirement at Pencey Prep.
From his behavior, it is clear that he has no respect for the sport that he is responsible for managing, is easily distracted and uninterested in his obligation to manage the equipment while on the train.
"I was the goddamn manager of the fencing team. Very big deal. We'd gone in to New York that morning for this fencing meet with McBurney School. Only, we didn't have the meet. I left all the foils and equipment and stuff on the goddamn subway. It wasn't all my fault. I had to keep getting up to look at this map, so we'd know where to get off." (Salinger)
Holden does take partial responsibility for the equipment being left on the train, but clearly does not understand that the whole problem is his fault.
He mocks the process of competition when he says that he is the "Goddamn manager of the fencing team, very big deal" he expresses this in a typical sarcastic way, the same way that he mocks the school, and everything about it.
He has no team spirit, he tells us that he just can't feel anything when he is standing on the hill far from the football game that is taking place on the field below. His description of the game also illustrates how he feels about competition.
"I was standing way the hell up on top of Thomsen Hill, right next to this crazy cannon that was in the Revolutionary War and all. You could see the whole field from there, and you could see the two teams bashing each other all over the place." (Salinger)
Holden's description of competition sounds more like a battle between two sides rather than a sport. He doesn't see the purpose in competition, especially in a game. Holden has more important issues on his mind that is why he has little interest in sports, competition or academics.