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What I was really hanging around for, I was trying to feel some kind of 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. (1.8)
This introduces us to a central paradox in The Catcher in the Rye. Holden wants to make connections with people (or, in this case, with places), but to do so means to make an emotional investment that will probably end up depressing him. Here, however, he seems to decide that he would rather feel sad about leaving a place than feel sad about the fact that he doesn't get to feel connected enough to feel sad. Make sense? Now compare this to the last paragraph of the novel, where Holden says not to tell stories, as you then miss the people in them. Does this mean he's changed his mind?
The minute I went in, I was sort of sorry I'd come. He was reading The Atlantic Monthly, and there were pills and medicine all over the place, and everything smelled like Vicks Nose Drops. It was pretty depressing. I'm not too crazy about sick people, anyway. What made it even more depressing, old Spencer had on this very sad, ratty old bathrobe that he was probably born in or something. I don't much like to see old guys in their pajamas and bathrobes anyway. (2.3)
Holden is depressed by physical illness, and we know from his hints that he's approaching a sort of sickness himself. If we're wondering whether he's gotten physically or mentally ill, this passage adds weight to the argument that there might not be too large a distinction between them.
After I shut the door and started back to the living room, he yelled something at me, but I couldn't exactly hear him. I'm pretty sure he yelled "Good luck!" at me. I hope not. I hope to hell not. I'd never yell "Good luck!" at anybody. It sounds terrible, when you think about it. (2.78, a.k.a. the last paragraph in the chapter)
Part of listening to Holden talk is trying to understand why he finds all these things depressing. Wishing someone "good luck," for example, might "sound terrible" since it implies he's not doing so well and needs it.