The point that Holden is trying to make when he elaborates about suitcases is that people judge others by the kind of suitcases they carry. He says,
"...it's really hard to be roommates with people if your suitcases are much better than theirs - if yours are really good ones and theirs aren't. You think if they're intelligent and all, the other person, and have a good sense of humor, that they don't give a damn whose suitcases are better, but they do. They really do".
Holden is talking about prejudices that are deeply ingrained in people. Having a nice suitcase identifies an individual as belonging to a high social class, something to which most people aspire even while pretending that they don't. Holden remembers the example of an old roommate at Elkton Hills, "Dick Slagle, that had these very inexpensive suitcases". Dick used to hide his suitcases, even as he made fun of Holden's expensive suitcases for being "too new and bourgeois". Feeling bad for Dick, Holden began to hide his own suitcases so as not to show his roommate up, but Dick kept taking them out again. As it turned out, Dick wanted Holden's suitcases to remain out on display so that people would think Holden's bags were his.
Ironically, even though Holden says he hates the way that suitcases seem to define people, he himself is guilty of the same prejudices. When he sees the nuns come in carrying "very inexpensive-looking suitcases", Holden is repulsed. He says,
"It isn't important, I know, but I hate it when somebody has cheap suitcases. It sounds terrible to say it, but I can even get to hate somebody, just looking at them, if they have cheap suitcases with them".
Although it might be argued that Holden's aversion to people with cheap suitcases stems from his experience with Dick Slagle and so does not indicate a prejudice based on class, it is a prejudice nonetheless. Like the bigoted people he knows who judge others by the kind of suitcases they carry, Holden too "can...get to hate somebody" just because "they have cheap suitcases with them" (Chapter 15).