The word "friendship" is important concerning the relationship between Amir and Hassan. Amir can never quite bring himself to call Hassan his friend: Because of his lowly Hazara heritage, Hassan is relegated to a second-class status in Kabul, and Amir cannot get past this division of society. Instead of following his heart, he listens to the taunts of soldiers and schoolmates, who constantly remind him of Hassan's and Ali's role as servants and not equals. Part of Amir's philosophy comes from Baba.
... in none of his stories did Baba ever refer to Ali as his friend. (Chapter Four)
And as a young child, Amir feels especially close to Hassan.
... we were kids who had learned to crawl together, and no history, ethnicity, society or religion was going to change that either. (Chapter Four)
Amir spends all of his free hours away from school with Hassan, telling him stories and flying kites, and the two are virtually inseparable. But peer pressure and jealousy cloud Amir's vision, and when Hassan is forced to defend Amir from Assef and his thugs, Amir wants to tell them that
... he's not my friend!... He's my servant! (Chapter Four)
Although Hassan is Amir's servant, the Hazara boy also serves as Amir's protector, and when Amir's cowardice prevents him from coming to Hassan's aid when he is sodomized by Assef, Amir can no longer live with Hassan serving as a daily reminder of his actions. It is only many years later that he comes to realize that Hassan was more than a servant: Hassan was Amir's friend--and his brother.