One important quote from Amir in The Kite Runner is the following:
I always felt like Baba hated me a little. And why not? After all, I had killed his beloved wife, his beautiful princess, hadn’t I?
What’s important about this quotation is that it helps us to understand the fraught relationship between Amir and his father, Baba. Amir has always felt that Baba resents him for causing the death of Baba’s late wife and Amir’s mother, who died in childbirth. And so, Baba has never been able to show the necessary affection toward his son, preferring to show it instead to Hassan, his illegitimate son.
There is an element of hypocrisy here, as Baba cheated on his “beloved wife, his beautiful princess”; so perhaps, in treating Amir as less than a son, he’s transferring some of the guilt he feels for committing adultery.
Because Amir feels that his father hates him a little, he’s all the more determined to win his approval, which he attempts to do by winning the local kite-flying tournament. If he cannot have Baba’s affection naturally, then he can at least earn it.