How does the theme of appearance vs. reality lead to Amir's downfall in The Kite Runner?
In speaking of Amir's "downfall," I assume you are referring to Amir's betrayal of Hassan when they were boys in Afghanistan, but you might be referring to Amir's jealousy and insecurity as a boy. The conflict between appearance and reality, however, plays a role in both of these situations. While he is growing up, Amir suffers as the result of false assumptions on his part. It appears to Amir that his father does not love him. Amir internalizes what he perceives to be a lack of love, coming to feel that he is unworthy, that he lacks whatever it is that would make him acceptable to his father. It is only after making their dangerous escape from Afghanistan and settling in California that Amir grows close to Baba and realizes that his father does love him and has always loved him, even when he seemed to expect a great deal from Amir.
Also, while he was growing up, Amir had no way of knowing Baba's real relationship to Hassan. To Amir, it appeared that Baba loved Hassan more--or at least as much--as he loved his own son. Baba's affection and kind treatment of Hassan, who was only a servant, made Amir feel even more rejected by his father and even more insecure. Again, only after growing up does Amir learn the truth: Baba treated Hassan like a son not because he loved him more than he loved Amir, but because Hassan was his son, just as Amir was his son.
While he was growing up, what appeared to Amir as being the truth was, in fact, not reality. Being deceived by appearances, Amir grew up feeling insecure, angry, and ashamed--feelings that led to his betrayal of Hassan by forcing him out of their home.