The answer is quite simple: because it provides further context to better understand the character’s backgrounds, which inevitably influence their choices and motivations.
Historically: the Soviet Invasion of Afghanistan provides insight into how chaos took hold and destroyed Afghanistan, and this destruction is depicted from both the macro level (the country’s history) to the micro level (the personal history of the characters), with Amir who becomes a refugee in the US, Hassan that becomes a war victim and Assef that becomes a Taliban p e-dophile warlord.
Culturally: Afghanistan, due to its strategic position is a multicultural and multiracial crossroad for several nations, empires and religions. Amir is a Sunni Muslim of the Pashtun Ethnic-linguistic group. They are to some extent white and do speak an Indo-European language.
Hassan is actually a Hazara, racially not white and actually descended from the Mongolian-Turkish invaders. They speak a different language, the Hazaragi which is Asian-Turkish-Mongolian and they are actually Shia Muslims. It is very easy for someone with basic knowledge of Asian and Islamic history to detect the sources of cultural, religious and/or racial conflicts.
Amir has been raised by his father to be more of a secular Sunni Muslim, far more westernized than Assef who belongs to the same religion and racial group. When Amir asks his father about sin, the latter provides him with a very secular definition, highly critical of Sunni Islamic orthodoxy, which explains why they would have to flee the country since the Afghan rebels that fought the Soviets were very orthodox and radical Muslims who would not hesitate to kill him and his family for holding such views.
This religious and cultural context also explains why it was so difficult for his father to reveal to his son that he had had an affair with Hassan’s mother and that he was Amir’s half-brother since such actions are both a religious, racial and cultural transgression. The Shia and the Sunni Muslims have been killing each other for millennia.
Assef is a Taliban, an orthodox form of Sunni Islam and he is also a p edo-phile and a r acist warlord. He hates Amir not only because he is secular and westernized but because he perceives his friendship with Hassan as an act of betrayal to their common tribe.