Holden has just gotten kicked out of Pencey Prep in PA. He has failed 4 out of 5 classes. He passed English because he is able to freely express himself.
Holden's failure to apply himself and his inability to come to terms with the "phoniness" of the adult world is seen once he fails out of Pencey Prep.
Right before this scene occurred, Holden took off his red hunting hat which serves as a form of protection against growing up and the adult world. It also serves as a form of alienation between Holden and growing up/ the adult world.
Did you have sex with Jane, Stradlater??
Now shut up, Holden, God damn it-I'm warning ya!
Will you go to Vermont with me and live in a cabin? You give me a royal PAIN IN THE ASS!
Holden's rough ending with Sally is evident in the theme of the pain of growing up. Holden's inability to deal with rejection and lack of logical thinking makes him not be able to understand the process of growing up.
Holden wants children to maintain their innocence, and a good example of that is Phoebe's notebook, which contains pure truth about everything and the least amount of phoniness. This characterizes Phoebe's notebook as a symbol.
Holden's interaction with Antolini suggests that Holden still isn't quite content on the idea that adulthood scares him and also puzzles him. He instead creates the reality that the world is full of all fake and hypocritical things, most often described as "phony".
Holden is trying to preserve Phoebe's innocence and youth. Her reaching for the golden ring symbolizes her reaching for maturity. He realizes that Phoebe is growing up and he can't protect her from that. This is the only time in the whole book that Holden says he is happy. He is happy watching Phoebe on the carousel.