Although Amir was a good kite fighter--he had once finished in the top three in a previous tournament--he had never won a tournament as Baba had done when he was younger. When Baba casually announced that "I think maybe you'll win the tournament this year," Amir realized that it was a goal he must accomplish. Not only would he be able to match Baba's feat (he had once cut 14 kites on a single day), but he would be able to make his father proud of him--and forgive him.
I was going to win... to run that last kite. Then I'd bring it home and show it to Baba. Show him once and for all that his son was worthy.
In Amir's mind, it was the only way that he would be able to impress Baba. If he won the contest, Baba might realize that his writing skills were important.
Maybe Baba would even read one of my stories... Maybe he'd call me Amir jan... And maybe, just maybe, I would finally be pardoned for killing my mother.