How could The Catcher in the Rye be considered as a tragedy?

The Catcher in the Rye details a manic three-day period in which Holden Caulfield's life slowly unravels, leading to a mental breakdown and a stay in an institution. The story deals with serious subject matter, including depression, isolation, death of a sibling, and inappropriate teacher advances, and Caulfield's veiled cries for help are likely to invoke pity in readers; these details indicate a work of literature that can certainly be categorized as a tragedy.
Caulfield is a self-conscious, ill-adjusted narcissist who is traumatized by the death of his brother Allie and is incapable of fitting in at the various boarding schools he attends. His narrative displays the confusion and conflict within, and he contradicts himself often by detailing the beauty of life, followed closely by the terrible misery of life. Caulfield expresses disdain for things and people that are phony, yet he himself lives in an alternate reality, distracted and discontent. He looks fondly upon the past and upon his innocent siblings (Allie, who died young, and Phoebe, who is still young), but he finds few other people who meet his high standards and finds little else in life that brings him satisfaction.
Holden Caulfield ultimately desires to escape the depressing aspects of life, discover his true identity, and simply be happy, a search that is in itself a tragedy since one cannot pause and appreciate real beauty while seeking a mythical ideal. His search for identity is realistic, easily resonating with adults of any age, and we can consider his institutionalization after the events in the novel to be the main character's downfall, which aligns perfectly with the tragedy genre.

A tragedy is a type of drama that deals with serious subject matter and presents human suffering in a dignified manner. According to Aristotle, tragedy is an "imitation of an action that is admirable" and "possess[es] magnitude." A tragedy must also induce pity and sadness from the audience, and the objective of Greek tragedies is for audiences to experience catharsis, which is an intense release of emotions. While The Catcher in the Rye does not fit the traditional Greek standards of a tragedy, it does depict Holden Caulfield's tragic downfall as he experiences a mental breakdown.
Holden is a severely depressed, jaded adolescent who feels isolated in the world and will soon be forced to enter adulthood. Holden's journey deals with serious subject matters that include death, suicide, sexual tension, and pedophilia. Holden talks about his brother Allie's death at the tender age of eleven, recalls witnessing James Castle's mangled body after he commits suicide, and has a strange encounter with Mr. Antolini, who seems to be making a pass at Holden while he sleeps. Towards the end of the novel, Holden mentions that he feels as if he will disappear every time he crosses the street, and he even loses consciousness. Holden's story also ends on a rather disappointing note, with Holden being admitted to a mental hospital or sanatorium. Overall, Holden's depressing story deals with serious subject matters and has a tragic ending that corresponds with Holden's mental breakdown.