In addition to the previous post, it is the son's rebellion against the father's paranoid, overprotective parenting that is the turning point in the novel which leads the son to salvation in the end.
There are two turning points in the novel: 1) the boy is nearly taken hostage; 2) the father takes the man hostage. Both of which lead up to the resolution: the survival of the boy and "the fire," indeed, of all future generations.
In the first scenario, the father is right. Neither he nor the boy should have trusted the barbarian. The man was right to shoot him. If he hadn't, they both would have been dead. The boy learns not to trust groups of men--bands of marauders, cannibals.
In the second scenario, the boy is right. Here, the father plays the role of the barbarian: he takes the man hostage. The father mistakenly takes the same defense against the solitary man on the road as he does against the marauding groups of men. Here, the boy learns that he can trust a solitary man. Solitary men "carry the fire." They are prophets, so to speak.
Luckily, the solitary man does not have a gun or friends; otherwise, they might both be dead. But it is the son's compassion ("the fire") for the man that spares his life. The father's fire is extinguishing: he has little compassion left, and he soon dies thereafter. But the boy trusts the man and convinces his father to let him go. The boy's instincts are rewarded: the man walks on without incident.
This all leads up to the resolution: when the boy encounters the man with the shotgun on the road after his father dies. If the boy had followed his father's advice to turning point #1, he would have been killed or never found. He would have been shot or run away. Fortunately, the boy has compassion and trust left in mankind ("fire"), and so he walks out on the road. His decision not to run away or fire on the man with the shotgun allows him to be rescued, to unite with a family, and to "carry on the fire."
The father has to make many difficult decisions in the course of every day as he and his son battle for surivival. A lot of these decisions seem to be harsh and cruel at the time, but they are all done in the name of helping to teach his son valuable lessons about survival, and about the importance of maintaining human decency. They are difficult lessons to teach, because they are seemingly contradictory.
Whenever they come across a survivor, the father urges the son to keep walking, and not to help; this harsh edict come from the father's fear of the barbrians that roam the land. He is worried that survivors are the bait to lure innocent people in, or that they are vicious themselves. The son, each time, is devastated; he wants to help, he can't stand to see people suffer. But the father is insistent, and in most cases, is wary, trying to teach the son that they can't trust other people inherently.
A very difficult decision the father has to make is to kill the man that discovers them in hiding; he is a barbarian, and intent on killing them for food. The father, with limited bullets, and with his son right there by his side, decides to shoot the man, right then and there. That decision exposes his son to brutal gore and horror, right in front of his eyes. But, it is a crucial lesson for the son to learn--protect yourself at all costs. There are ugly, mean things in the world, and to surivive it, you have to make tough choices. The son learns that you cannot trust people on sight, and that will be a lesson that he takes with him, that will hlep him to survive the harsh world that they live in. I hope that helps; good luck!