How does the father's mental state affect the decisions he makes?
In Cormac McCarthy's The Road, the father must overcome extreme mental and physical duress in order to survive and "carry the fire" (keep his son alive). The man knows he will die soon (he's inhaled so much ash), and he faces the existential dilemma that he and his son are the only "good guys" left in a godless universe ("There is no God and we are his prophets") filled with cannibals and marauders. On top of it all, keep his son's faith and spirits high.
First and foremost, the father must deal with the problems of suicide and mercy killing in order to protect his son from cannibals. Worse, the father has only two bullets in his gun: one for him, one for his son. But, he after he shoots a marauder, the one bullet leaves him with a mental quandary: teach the son to shoot himself while the father fights the cannibals to the death. Needless to say, these options would drive anyone to mental breakdown:
He waited. The small nickelplated revolver in his hand. He was going to cough. He put his whole mind to holding it back. He tried to listen but he could hear nothing. I wont leave you, he whispered. I wont ever leave you. Do you understand? He lay in the leaves holding the trembling child.
In addition, the mother has already committed suicide, and the father has terrible flashbacks about their past life before the Apocalypse:
In his dream she was sick and he cared for her. The dream bore the look of sacrifice but he thought differently. He did not take care of her and she died alone somewhere in the dark and there is no other dream nor other waking world and there is no other tale to tell.
Ultimately, the man suffers from extreme paranoia: he believes the road is not safe for travel. He cannot tell the present from the past. Time and again he urges the son to stay off the road and hide in the woods. He fears that he will not get the boy to safety and warmer climes before his death. Ultimately, it his son's overcoming his father's fear after he has died and going onto the road that saves the boy. There, he meets the man with the shotgun and joins his family. So, the son's faith (the very opposite of father's mental problems) is what saves his live and humanity.