The reason is quite simple: because of the necessity of the plot completing the main character’s arc by an act of redemption, which is one of the main themes of the novel.
Indeed, Amir does not really need to return to Afghanistan, he lives a successful and happy life in the USA as a novelist, yet he is lacking something important which compels him emotionally and psychologically to go back to a dangerous, war-torn country. That something is redemption which is proven by the sentence Hassan’s father utters when he contacts him: "There is a way to be good again."
And that way is to save Sohrab, Hassan’s son from both the Taliban regime and Assef, the child predator. Hassan is dead because he is the symbol of a wound that can never be fully closed. What Amir did to him was unforgivable and has haunted him for years. Sohrab is a second chance for Amir to do the right thing he failed to do when he was a child and to finally be brave and risk his life for a good cause. Assef is the symbol of the past that is always present to Amir through his guilt.
Their final encounter mirrors the past in that Amir finally stands up to Assef how he should have in the past and by doing that he redeems himself and is yet again saved by Hassan in the form of his son Sohrab who fulfills the promise (or even prophecy) that Hassan had made to Assef, that he would use his slingshot to shout out his eye with it. In this manner, the character arc and the plot reach their conclusion.
