Why does Holden watch the game from the hill in The Catcher in the Rye?

When the novel opens, Holden is standing on top of a hill looking down at the football players and the fans. He gives two reasons why he is on the hill rather than down at the game, but neither reason is entirely satisfactory. The first reason is that he has been "ostracized" by the fencing team for losing all their equipment in New York. Holden is, or was, the manager of the team and responsible...

When the novel opens, Holden is standing on top of a hill looking down at the football players and the fans. He gives two reasons why he is on the hill rather than down at the game, but neither reason is entirely satisfactory. The first reason is that he has been "ostracized" by the fencing team for losing all their equipment in New York. Holden is, or was, the manager of the team and responsible for the foils, masks, and other fencing equipment. This hardly explains why he has gone up to the top of Thomsen Hill, though. More likely, Holden feels ashamed of himself and wants to be alone. If he were to join the crowd watching the game, word would get around that he had returned early because the fencing match had to be called off and that he was responsible. Holden's descriptions of his last days at Pencey reveal that he is an outsider and a loner even without being "ostracized." He doesn't appear to have a single friend at the school. This is partly because he is known to be flunking practically all his courses. Many of the students must already know that Holden has been expelled. 

Holden says that his other reason for being up on Thomsen Hill, or at least not at the game, is that he is on his way to visit his history teacher Mr. Spencer, who is confined to his bedroom with the grippe. This hardly seems to explain why Holden would have climbed a hill to get to Mr. Spencer's home. Holden's real reason becomes apparent when he says,

Only, I wasn't watching the game too much. What I was really hanging around for, I was trying to feel some kind of a good-by. . . I mean I've left schools and places I didn't even know I was leaving them. I hate that. I don't care if it's a sad good-by or a bad good-by, but when I leave a place I like to know I'm leaving it. If you don't, you feel even worse.

Holden has already flunked out of two other prep schools. He obviously feels miserable. He will have to face his parents and be made to feel even more miserable for disappointing them. It is difficult to understand this boy because he doesn't even understand himself. It is easy to commiserate with his feelings, though. He has nobody to say good-bye to because everybody dislikes him, with the possible exception of old Mr. Spencer, who sent him a note asking him to come and see him before he leaves for his home in New York City. That meeting takes place in Chapter Two, and it doesn't make Holden feel any better. It turns into a lecture from an old man in a room that smells of Vicks Nose Drops. By the time Holden gets through describing a few of his other acquaintances at Pencey, it isn't hard to understand why he makes the sudden rash decision to stop just "hanging around" and leave for New York immediately.