Booker says that in the "falling stage," the hero is "underdeveloped" and in the shadow of something "dark" that may "spring entirely from within the hero's own personality." Yep. Sounds about right to us. By writing off everyone around him as "phony bastards," Holden makes it impossible for himself to ever connect with another person.
In this stage, the "dark" power seems to have receded. Hm. This one's a little trickier, but it still seems to fit: Holden thinks that by leaving Pencey, he can leave behind the phonies and embrace a more genuine, open life. And when he gets to New York, he definitely does call up old friends (and make new ones).
A more genuine open life? On second thought, maybe not. Holden is basically imprisoned by his own judgmental tendencies. Even when he reaches out to others, he's still mentally rolling his eyes at them. Case in point? The three "morons" from the Lavender Room.
Even if you think the Mr. Antolini incident wasn't sexual, it still works as the Nightmare Stage. Look at it this way: if Mr. Antolini is coming on to Holden, then the one adult he was really starting to connect to turned out to be doing so for selfish and extremely questionable ends.
And even if Holden only imagined the friendly gesture as a sexual come-on, then this is just a continuation (and in fact, a powerful resurgence) of the same "dark power" that has a hold on Holden from the start. Holden is imprisoning himself from Mr. Antolini's friendly advances because of his own judgmental and suspicious mind.
Booker says the Rebirth Stage consists of the hero being freed by a young woman or child. And that's literally what happens: Phoebe saves Holden.
But how, exactly? Well, she's the only person in the novel to have a genuine and compassionate conversation with our protagonist. When he cries, she puts her arm around his shoulder. She lends him her money. She covers for him when their parents get home.
And then there's that carousel scene. Phoebe gives Holden his hunting cap back when it starts to rain, showing that she cares about him and his individuality. And she helps him realize that the process of growing up and "losing innocence" doesn't have to be a dark and scary one: kids have to grab for the gold ring, even if they might fall off their horses.