How is the beginning linked with the ending in The Kite Runner?

This is a great question. One of the key episodes at the
beginning of the novel, when Amir and Hassan win the Kite competition and Hassan captures the
kite, is mirrored at the end of the novel but under radically different circumstances, as the
roles have reversed entirely.

At the end of the novel, it is Sohrab
who wins the competition and it is Amir who runs after the kite for him, and it is also Amir who
finds himself saying what Hassan said to him all those years
ago:

"For you, a
thousand times over," I heard myself
say.

At the beginning of the novel,
this comment is indicative of the deep love and friendship that Hassan has for Amir, which
tragically he goes on to betray so terribly as he does nothing to prevent Hassan from being
raped. At the end of the novel, however, it is symbolically significant that Amir says this to
Sohrab, indicating how far he has travelled during the course of the novel and how he has changed
from a selfish, spoilt boy to a man who is brave enough to love and receive love in turn. Thus,
his comment at the end of the novel shows how he has transformed himself. It is also significant
to note that it is this episode that represents the first breakthrough into Sohrab's character
and makes him smile.