Birdy doesn't even make it to Fallujah, the Iraqi town mentioned in the title, until more than halfway through the book. Our main man spends more time in places like Baghdad. So why does this particular town (at sunrise) get a title cred?
Because although crazy, intense things go down in all of Birdy's missions, in Fallujah it gets up-close and personal.
Birdy catches Miller about to get raped, and he shoots the two men trying to rape her. On one hand, he prevented something awful from happening, but on the other, he literally blew two peoples' brains out.
That's why his ride back to camp is title material. It's different from all the others:
But here, on this bright morning, I rode for the first time as someone who had killed. All the times before that, I had fired my weapon into the darkness, or some fleeting figure in the distance. I could say that maybe I had missed, that maybe it was not my bullets that hit them.
No more. I wanted to be away from Fallujah, away from Iraq. I wanted to be alone in the dark with my grief. I wanted to mourn for myself. (14.140-141)
Even though there's a beautiful sunrise—the world is moving on, like nothing happened—Birdy has changed. Now that he's killed, he's a different man now, and he can never go back to the person he was before.