Interesting question: when you have a framed story (as you do here, with seventeen-year-old Holden telling the story), how does that fit into a Classic Plot Analysis? We think that the initial situation is Holden, wherever it is that he's "resting up," introducing himself and beginning the story. But it also seems that the story Holden tells follows the Classic Plot in its own way. So that's what we're going with.
This is more of a book-long conflict than one specific event, but it is the friction that drives the novel along, so that's good enough for us. You can see where the discord comes in; it's hard to hate a person and want them to go get a drink with you at the same time, yet Holden seems to do this with every person he meets. You can see the intensity of his desire to understand and be understood in those times when he racks his brain for someone – anyone – to talk with (think about when he goes into the phone booth, but can't decide on anyone to call).
We start to get some hints that Holden isn't doing too well. Sally repeatedly asks him to not scream at her, though he insists he's doing no such thing. He gets smashingly drunk and walks around the park in the middle of the night looking for some ducks. Mr. Antolini's warning that he's in for a "special help" gets us all ready for the climax.
Here's a good one for you – does Holden's breakdown happen on stage or off, so to speak? We know he ends up having to go somewhere to rest up, and we know it has to do with the "madman stuff" that happened "around Christmas," but do we see it happen? Whatever "it" is, "it" is the climax. You could see the climax in Holden's physical deterioration – after the incident with Mr. Antolini (a sort of climax in its own right), Holden is extremely on edge. He talks aloud to Allie as he crosses the street because he's afraid he'll disappear. He passes out. Is this the "madman" stuff he's talking about? Or is there something else, some bigger climax we don't get to see, that lands him in therapy?
Now we're nervous. OK, we're not that nervous, since we know from the intro that Holden ends up "resting up" somewhere.
What's interesting about this denouement is that it doesn't start when Holden confesses he's not running away after all. It starts when Phoebe drags a big suitcase up and declares she's running away, too. Phoebe's adamant decision makes obvious the ludicrous nature of Holden's own plan – both to us and to Holden himself. We all realize it was a silly fantasy, have a good denouement-y laugh, and head on to the conclusion.
What is the conclusion of The Catcher in the Rye? We're not going to declare any one lesson learned. Holden leaves it ambiguous as to whether he's "better" now or not, and many would say there is no "better" anyway; he just has to grow up, painfully and with a lot of depression thrown in for good measure. On the other hand, we look to the last line of the novel for another take on the conclusion: "Don't ever tell anybody anything. If you do, you start missing everybody." Perhaps then, the conclusion to Holden's initial conflict (the tension between wanting to connect but hating everyone) is that he did in fact connect – in one way or another – with everyone he met. The new question isn't whether or not one should connect, but whether or not the pain of inevitable loss is worth the initial gain.