It is in chapter six that this analogy is drawn between kite flying and war. Note how Amir describes himself the night before the competition:
I felt like a solder trying to sleeep in the trenches the night before a major battle. And that wasn't so far off. In Kabul, fighting kites was a little like going to war.
As we understand more about the cultural significance of fighting kites, we see Amir's point of view. Fighting kites was a savage competition, where only the merciless and resolute triumph. It was also a way to gain honour and kudos by defeating your opponents. Remember how Amir hopes to win the favour of his father by triumphing in this competition. Reputations are gained and lost, and during the battle, great sacrifice is needed to ensure that you triumph. Note how Hassan's hands bleed with handling the cord. This analogy is not stretched very far at all.