"In one of those bars up and down that highway he left his doggy bag with his teeth just laying in the chop suey."
Austin recalls the story of going to Mexico to get his father after the man had all his teeth pulled. The statement alludes to their father giving up his right to speak even when he'd been given a new opportunity to do so, and in a way giving up his connection to his son.
"It's that time of the morning when coyotes kill people."
Austin says this to his brother Lee early in the morning while the coyotes are howling. He tells his brother that this is when they kill the dogs. The statement is a symbol for Austin and Lee also being in the midst of being killed. They are on the verge of killing each other as well as any dreams they have of writing a screenplay that will sell.
"This is the last time that I try to live with people, boy!"
Lee is trying to find a pencil or a pen in his mother's house and he cannot find one and begins to go berserk when he cannot find one anywhere. His statement is an explosion about the fact that when he has to rely on other people they always let him down, and this is why he stays in the desert all alone.