At times when Holden Caulfield feels exceptionally sad, he mentions the ducks in Central Park. Multiple times throughout the novel he expresses concern about where they go in the winter since the pond will be frozen. Being expelled from Pencey Prep triggers Holden to first think about the ducks. After berating himself for being absent-minded, he remembers and asks the taxi driver where he believes the birds go. Holden asks the question again to another taxi driver, who tells him ducks fly south for the winter. After an evening of drinking at the bar, Holden decides to search for the ducks himself. He can't find any, so he admits defeat. Then Holden reflects on his own death and how his family would react.
Holden Caulfield only asks about the ducks in Central Park because he is genuinely curious about where they go in the winter when the pond freezes over. Everyone he asks plays off the questions as absurd, and he is left without an answer until a cab driver tells him they fly south.
[P1] Holden Caulfield thinks about the ducks in Central Park when he is sad. [P2] Holden Caulfield uses the ducks to avoid his depression. [P3] Therefore, the theme of The Catcher in the Rye is mental illness.
Rejecting the premises
[Rejecting P2] Holden Caulfield thinks about the ducks only because he is curious about where they go when the pond freezes over.