The dog's leaving represents the harshness of nature and the animal's deep instinct to survive. When it first encounters the man, the narrator claims, "It was not concerned with the well-being of the man. It was for its own sake that it looked toward the fire" (London 70). Although a certain bond forms between the two figures, the dog leaves when it sees that it has no more use for the man (he is dead and therefore no longer maintaining a fire). It departs for other men who will provide for its needs in the camp. Although the narrator does imagine the dog's thoughts, it is clear that the dog is not a rational animal; rather, it is responding to its instincts. These same instincts and sharp senses also help the dog feel that something is awry when the man thinks about killing the animal for warmth. In that way, both man and animal are responding naturally to a survival situation in the harsh Yukon. The dog must return to civilization if it is to live; the scent of death forces the dog to leave the scene.
London, Jack. "To Build a Fire" 1908. https://americanenglish.state.gov/files/ae/resource_files/to-build-a-fire.pdf. Accessed 27 April 2018.