Despite Amir's longing for his father's love, attention, and approval, Baba is not a particularly supportive parent to Amir in The Kite Runner by Khaled Hosseini. Things are better between them after father and son leave Afghanistan; however, in Amir's growing-up years, Baba is not a nurturing parent. He is larger-than-life and full of dictates and mandates which are impossible for anyone to live up to, and we discover later that Baba does not live up to his own impossibly high standards. He provides materially for Amir, but he is emotionally absent for his son.
In that environment, the young Amir needs someone who will praise his small accomplishments and make a connection with him. For Amir, that person is Rahim Khan, his father's best friend and business partner.
While Baba is constantly spending time on business matters and ignoring his son, Rahim Khan is willing to spend time with the young Amir. Amir finds refuge in Rahim Khan's praise and friendship, and Amir makes it clear that he would have lived a doomed life if it were not for Rahim Khan:
As always, it was Rahim Khan who rescued me.
Later, when Amir is much older, Rahim Khan offers Amir another kind of rescue, relief from his guilt--"there is a way to be good again," he tells Amir.
While Baba reveals nothing about Amir's mother or anything about his own life (other than his exploits), Rahim Khan talks with Amir about things that matter to the boy. Rahim Khan shares a story about a girl he loved who was a Hazara and therefore unavailable to him. He tells Amir:
"You should have seen the look on my father's face when I told him. My mother actually fainted. My sisters splashed her face with water. They fanned her and looked at me as if I had slit her throat. My brother Jalal actually went to fetch his hunting rifle before my father stopped him." Rahim Khan barked a bitter laughter. "It was Homaira and me against the world. And I'll tell you this, Amir jan: In the end, the world always wins. That's just the way of things."
Not only is this self-revelatory, this story tacitly tells Amir it is okay to love someone who is Hazara (like Amir's friend Hassan) but affirms that it is also hard.
While Baba only praises his son when he does physical exploits like he did (wrestling a bear, for example), Rahim Khan praises Amir's writing and recognizes this talent, something Baba would never do.
Amir spends most of his childhood trying to please his unapproachable father; sometimes Amir is happy just to get Baba to notice him. He listens to his father's rules and tries to live up to them, but it is a virtual impossibility and he often fails. Baba is dismissive and even cruel to his son, and he fosters jealousy in Amir by being kind and generous to Hassan.
Rahim Khan is the constant in Amir's life. He is non-judgmental (even though he has every right to be) and supportive of Amir. Their relationship continues after Baba dies, and Rahim Khan trusts Amir with something his father never did: the knowledge that Amir and Hassan are half-brothers. While Rahim Khan understandably wants Amir to rescue Sohrab, Hassan's son, he offers Amir the first opportunity to do so, knowing Amir is still suffering guilt from his childhood.
Rahim Khan is strong, loyal, and kind; he is the consistent moral presence in Amir's life. Without him, Amir would have lived his entire childhood either under Baba's disapproval or without being noticed at all. He is Amir's refuge and rescuer.