says this because he thinks that Amir and he have nothing in common; Baba is the legend who supposedly wrestled a bear, and Amir is a sensitive, introspective writer who cannot defend himself or Hassan. Despite this comment, we know that Baba is Amir's biological father.

Hassan's paternity, on the other hand, comes into question later in the novel, when Amir returns to the Middle East as an adult at Rahim Khan's request. Rahim Khan is dying and wants to give Amir the opportunity to redeem himself ("There is a way to be good again."). During this conversation in Chapters 16 and 17, Rahim Khan reveals that both Ali and Hassan are now dead, but that Hassan's son Sohrab is in an orphanage and needs Amir's help. In order to motivate Amir to go to Kabul to save Sohrab, and thus, to amend for the wrongs committed against Hassan when he and Amir were children, Rahim Khan reveals that Ali was sterile and Baba is Hassan's biological father. Rahim Khan tells Amir that Ali was married once before and after his wife left him, she had three children with another man; Ali was not able to conceive a child. Amir struggles to understand but finally does infer that Baba was indeed Hassan's father. Amir is furious that his father and Rahim Khan kept the truth from him and from Hassan, who can now never know the truth; Amir accuses his father of committing the sin Baba had told Amir was the worst of all: theft. Baba stole their right to the truth and stole Ali's honor by sleeping with his wife. Rahim Khan explains that it wouldn't have been possible given the social norms to have Hassan's paternity become common knowledge. Amir is now able to look back on Baba's treatment of Hassan -- his always wanting to bring Hassan along when he and Amir were going to spend time together, his buying Hassan expensive birthday presents like the harelip surgery, his grief when Hassan and Ali left the house after Amir framed Hassan for stealing -- and understand why Baba went above and beyond what a master would normally do for a servant in his treatment of Hassan, his biological son. 

Ali raised Hassan as his own, and though it is never explicitly stated that he knew that the boy was not his biological son, it is implied in the novel that he must have known he was sterile. After discovering that Hassan is his half-brother, Amir's guilt at what he did as a child is amplified, as he now feels he is responsible for his brother's death, too. This gives Amir the motivation to rescue Sohrab, despite the many obstacles and hardships they both must endure, and eventually adopt him and bring him to California at the end of the novel. 

In the novel, Hassan was the result of Sanaubar (Ali's wife) and Baba's adulterous relationship. Since Sanaubar was already Ali's wife at the time Hassan was born, all the parties involved simply continued with their lives as if the affair never happened. This was presumably done to protect Baba's position in his Pashtun/Sunni Muslim community. After all, Sanaubar was a Hazara (like her husband, Ali), and Hazaras were Shia Muslims; it would have been unthinkable for a man of Baba's position to admit to an affair with Sanaubar, a member of a hated sect.

After Sanaubar left Ali, he continued to raise Hassan as his own son. In the middle of the novel, we learn Hassan's true paternal heritage from the conversation between Rahim Khan and Amir. Rahim Khan confessed to Amir that Ali had always been sterile and that Hassan was fathered by Baba. Amir's reaction was explosive:

"You  bastards,"  I  muttered.  Stood  up.  "You  goddamn  bastards!"  I   screamed.  "All  of  you,  you  bunch  of  lying  goddamn bastards!"

"How  could  you  hide  this  from  me?  From  him?"  I  bellowed.

"Please  think,  Amir  jan.  It  was  a  shameful  situation. People  would talk.  All  that  a  man  had  back  then,  all  that  he  was,  was  his  honor,  his  name,  and  if  people  talked...  We  couldn't  tell  anyone,  surely  you  can  see  that."  He  reached  for  me,  but  I  shed  his  hand.  Headed  for  the door.

After he learned the truth about Hassan's parentage, Amir felt even more beholden to Hassan. He realized that both he and his father betrayed Hassan in their own ways. This terrible knowledge led Amir to fight for Sohrab's freedom as a form of redemption.