Holden asks Ackley if he can sleep in his room, since his roommate is out of town. But Ackley refuses. Holden then asks if it's possible to join a monastery without being Catholic. Ackley gets annoyed. Holden leaves.
Even as he tries to have company, Holden is talking about escaping society. His loneliness and desire for alienation are at cross-purposes.
In the hallway, lonely and tormented by the suspicion that Stradlater may have had sex with Jane Gallagher, Holden decides to leave Pencey and hide out for a few days in New York City until his parents learn he's been expelled and then calm down a bit. He packs and puts on his hunting cap. Crying now, he shouts "Sleep tight, ya morons!" and leaves.
Holden's loneliness and anger about Jane possibly sleeping with Stradlater drive him to leave Pencey, his society, to be alone in New York. His crying indicates something more than just typical teenage sadness, something more like depression.