Holden’s relationship with Jane is rather curious. Jane never actually appears in the story, but Holden frequently thinks about her. She seems to be the one girl - indeed, the one person - of his own age whom he genuinely likes. He remembers her as a quiet and caring kind of person, who has also suffered from a ‘lousy childhood’(chapter 4). This is one of the things that probably makes him more protective of her – he physically attacks Stradlater after Stradlater has been on a date with her. He is appalled at the very thought of Stradlater being with her, but we cannot be entirely sure if Stradlater is really as unscrupulous as he fears or whether his overreaction is more indicative of his own desire for her, which he doesn’t seem to want to acknowledge too much.
Holden, then, regards Jane as a close friend and is probably deeply attracted to her. However, he can never bring himself to even phone her. This may be because she functions as an idealized female figure for him to some extent, and he can’t cope with actually meeting her.
Jane is not infallible in Holden’s view, however; he recalls her once dating Al Pike, ‘a terrible guy’, ‘a show-off bastard’ (chapter 18), and afterwards resolutely sticking up for him:
Jane said he wasn’t a show-off. She said he had an inferiority complex. She acted like she felt sorry for him or something, and she wasn’t just putting it on. She meant it. (chapter 18)
Holden appears amazed that ‘even smart girls’ like Jane fail in judgement when it comes to conceited guys like Al Pike (chapter 18). Maybe this is his way of saying that Jane doesn’t appreciate him, Holden, quite as much as she ought to, and that is why he puts off meeting up with her.
Jane Gallagher is basically Holden's "the one that got away." He clearly had feelings for Jane -- not Jean, as he emphasizes -- Gallagher, evident by the fact that he keeps asking about what she's doing. He also vividly remembers the detail that she used to keep all of her kings in the back row and is aggravated by the fact that Stradlater has not seemed to notice details about Jane Gallagher that Holden himself has.
The fact that Holden also remembers these kinds of details and won't let go of them also is pre-emptive to how nostalgic Holden can be later in the novel (at the museum, for example, or as far as Allie's baseball mitt). It also shows us how emotional Holden is, and that he has a hard time letting go of things.