Holden Caulfield is traumatized by the death of his younger brother Allie. He died four years previously of leukemia, and Holden believes it is unjust. He mentions to readers that he wishes he would have died instead of Allie. At the time of Allie's death, Holden mentions he was almost "psychoanalyzed" because he was breaking windows. It is clear to readers that he is grieving over his brother and he does not know how to outlet his emotions in a healthy way. Throughout the novel, Holden continues to mention Allie to readers. His death was greatly influential and is a cause for his mental illness.
Even though Holden mentions Allie multiple times, death is not the main theme of the novel. None of the characters die, and Holden is more focused on his depressive feelings than traumatizing deaths from the past. Death is important in The Catcher in the Rye, but it is only a factor in the overall plot of the novel.
[P1] Holden Caulfield is grieving over the death of his brother, Allie. [P2] Holden is depressed because he is traumatized by his brother's death. [P3] Therefore, the theme of The Catcher in the Rye is death.
Rejecting the premises
[Rejecting P3] Death is only a factor in the background of The Catcher in the Rye.