This is a really good question. There can be several antagonist in this book. Each character, in some way or another, has a dark side to them, but is one darker than the other? This is the question we need to ask. From the first page of The Kite Runner, we are told that something happened twenty-six years ago and that Amir has tried to bury it.
That was a long time ago, but it's wrong what they say about the past, I've learned, about how you can bury it. Because the past claws its way out. Looking back now, I realized I have been peeking into that deserted alley for the last twenty-six years.
Amir, although he is the protagonist, he can also be seen as the antagonist. If Amir had spoken up for Hassan all those years ago, maybe things would have been handled differently. Amir had a way of cowardice and this affected many people. Amir spends most of the book trying to right the wrongs done in the past. Although Amir can be seen as the antagonist, Assef is one of the main antagonists of the story.
Assef was nothing more than a bully. He terrorized Amir and Hassan and got away with some really horrible things. When Assef rapes Hassan in the alley, it makes the point that Assef is the antagonist. He ruined not only Hassan's life, but many others as well.
Baba, Amir's father, can also be seen as an antagonist. In my opinion, Baba is the one who had wronged both Amir and Hassan. If Baba had been honest about who Hassan really was, maybe Hassan's life would have been different.
There are many people in The Kite Runner who can be called the antagonist. When you read the story you can see the many different ways each person carries their darkness, and how that darkness can have a life long affect on many people.
This is a complex question. There are several different answers that can be given. So, let me give you a few points for consideration.
First, on the most basic level we can say that Assef is the antagonist. He is the bully that took advantage of Hassan, and he is the one who created fear in Amir. Moreover, it was on account of him that Amir drifted from Hassan.
Second, we can say that the Taliban is also the antagonist, because it was their intolerant rule that caused so much of the grief in Amir's life, not to mention Baba's life.
Finally, we can say that Amir was the antagonist (as well as protagonist), because this is a story of redemption. Amir had to make things right by facing his past and demons.