When looking at the book The Kite Runner through the archetypal lens you see that family is the underlining factor that influences everyone to do things.
This affects Amir the most, being that he is the main character. Amir, who belongs in the Reluctant Hero archetype, is affected in many ways. First would be Amir not stopping Assef from raping Hassan, so he could get the kite. And secondly getting Sohrab back to America from Afghanistan. Amir's main relationship with his father is poor. Baba, Amir's father, blames Amir for killing his wife during Amir's birth. Of course there is no way Amir could have done this, but it makes no difference to Baba. Amir, being his son, wants to prove himself to Baba. This is exceptionally difficult for Amir because Baba is what most men strive to be. Baba has had many things to be proud of, such as running a profitable business or winning kite tournaments.
Of these things Amir can do only one: win the tournament. After Amir and Hassan win the tournament Hassan goes off to run the kite for Amir, when he does not come back Amir goes after him and finds him in an alley surrounded by Assef and his friends. Amir could have jumped in and saved Hassan but instead he lets Hassan get raped so he can get the kite to show it to Baba and to prove to him that he is in fact a good son. The fact that he lets Hassan get raped torments him for many years. In this time Amir moves to America, marries Soraya, and Baba dies. Not long after, Rahim Kahn calls Amir and tells him that Hassan has a son that he needs Amir to rescue.