In the novel "The Road" how does the antagonist affect the son's decisions or thinking?
It depends on what you call the antagonist; there are several possibilities. If the antagonist is the hopelessness of the world that they live in, then the son bears up remarkably well. He tends to have more compassion and hope than his father does, and maintains a faith in the goodness of people, despite the awful circumstances that they live in. If the antagonist is the cannabilistic barbarians that they run into occasionally, that threaten their lives and safety, he doesn't bear up so well. He is terrified of these horrific creatures of humans, and visibly and deeply disturbed by their barbarism. When they find the prisoners being harvested for meat, the son can't stand the thought of leaving them behind to be cruelly tortured to death by these people.
The son, despite the evidence of such awful human behavior and violence, is not completely disillusioned with people as a result like you might think he would be. To see such grotesque behavior from human beings would logically turn someone away from the belief that humans are worth saving at all. However, the son still holds out faith in the human race--he still wants to help survivors that he finds, he still believes that there are children like him out there, and that goodness is real. He is resilient in the face of any type of antagonism or despair. I hope that helps; good luck!