The man wants the boy to eat because he knows that he is not strong enough to survive, and there is not enough food for both of them.
The man’s only goal is to keep his son alive as long as possible. As the book ends, he has long accepted that he is going to die. He tries to give his son survival skills, and begins giving him more of the food as well.
They had for food a single tin of peaches but he made the boy eat it and he would not take any. I can’t, he said. It’s all right. (p. 277)
The boy feels bad, because he knows that his father needs to eat. His father is watching him eat not because he is hungry and wants the food for himself, but because he wants to see the boy getting healthier. He needs to see his sacrifice. This makes the boy very uncomfortable, which is why he asks his father to stop.
The Road is a love story between a father and son. The father makes the ultimate sacrifice, doing everything he can to keep his son alive—because he loves him.