In The Road's post-apocalyptic world that is "intestate," there is nothing to which the survivors can make claim. Therefore, the man is "the one" and only person to make a claim to the boy, and the boy has only his father between him and death. When the boy's innate charitableness manifests itself to the dying man and he wants to give him food, the father replies with practicality that there is no need to feed him because he is going to die, anyway.
The boy didn't answer. He just sat there with his head down, sobbing.
You're not the one who has to worry about everything.
The boy said something but he couldn't understand him. What? He said.
He looked up, his wet and grimy face. Yes I am, he said. I am the one.”
Thus, "I am the one" means that the man is the boy's only connection to life itself; without him, the child will not survive as he cannot find food and protect himself from "the bad guys," the predatory forces represented by the pillagers and cannibals. Truly, it is the father's love and devotion to his son that protects the boy.
Fire, of course, has long been a symbol of life and survival. It is also a reminder of the basics of life as the discovery of fire by prehistoric man was a boon as then people were able to stay warm against the elements and have light and something to cook their food. Against the ashes of their world, fire, therefore, signifies life and what it has meant in the past. Indeed, it is important to the boy that they "are carrying the fire" of what has been meaningful in their lives before the destruction. Frequently as they travel the road, the father relates tales of courage and justice from the lost world that will keep alive the fire of humanity in his son. This is done by the father in the desperate hope that there may be a future in which the boy can witness the harboring of the nobler ideals.
In the final pages of the novel as the father is dying, he tells his son that he no longer can be with him because he must "carry the fire."
Is it real, the fire?
Where is it? I don't know where it is.
Yes you do. It's inside you. It was always there. I can see it.
Then, when the man with his own children rescues him, the boy asks if he is "carrying the fire." At first, the man does not understand; then, he replies that he is,
"Yeah, we are....We have a little boy and a little girl."
His remark represents a Whitmanian optimism and faith in humanity's ability to survive. Much like Ma of The Grapes of Wrath the father and the boy's adoptive father believe in the power of their kind to "overcome" adversity:
"Us people will go on livin' where all them people is gone...We're the people that live. They ain't gonna wipe us out. Why, we're the people--we go on." (Ch. 20)
Certainly, the two symbols of The Road represent the power of love and virtue and the power of man's will to survive.