Holden calls Mr. Antolini. Upset that Holden has been expelled from another school, Mr. Antolini invites Holden to come stay at to his house. Holden describes Mr. Antolini as the best teacher he ever had. Mr. Antolini was the only person who even went near James Castle's body after he jumped out the window.
Mr. Antolini represents Holden's last hope: an adult he respects as non-phony, who, unlike other adults, tried to be a Catcher for James Castle. That's what Holden's looking for, someone to Catch him.
Holden convinces Phoebe to dance with him, but their parents come home. Holden hides in the closet until his mother tucks Phoebe in. After his mother leaves, he emerges and tells Phoebe of his plan to head out west. She gives him all her Christmas money ($8.65). He refuses to take it at first, then insists that she take his red hunting hat in exchange.
Phoebe thinks Holden is acting crazily, but doesn't judge. She supports him. She isn't phony. Holden handing over his hunting hat is symbolic: he's trying to protect his sister, and giving up protection for himself.