In "To Build a Fire," what point does London make by contrasting the dog and the man?
Well done for noticing the way that, throughout the tale, the man and the dog are contrasted to each other. Of course, the central contrast seems to be the way that the man is ruled by judgement and the dog by its instinct, which is a form of intuition that the man has lost log ago. Note what the text tells us about the dog and how he reacts to the cold, compared to the rational approach to the cold that the man adopts:
The dog did not know anything about thermometeres. Possibly in its brain there was no sharp consciousness of a condition of very cold such as was in the man's brain. But the brute had its instinct. It experienced a vague but menacing apprehension that subdued it and made it slink along at the man's heels, and that made it question eagerly every unwonted movement of the man, as if expecting him to go into camp or to seek shelter somewhere and build a fire. The dog had learned fire, and it wanted fire, or else to burrow under the snow and cuddle its warmth away from the air.
Note the way that they are contrasted here. The dog senses the danger of the situation and desires to follow its all important instinct to look for warmth, whereas the man refuses to recognise the danger inherent in the extreme cold, though he is able to use a thermometer and give a precise reading of the temperature. London is clearly showing the way that, in this situation at least, animal instincts are superior to human judgement and that we ignore such instincts as nature gave us at our peril.