2) Why does he come up with the "wild idea" to kill his dog? And what stops him from going through with it?
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The man is freezing to death:
He remembered the tale of the man, caught in a blizzard, who killed a steer and crawled inside the carcass, and so was saved. He would kill the dog and bury his hands in the warm body until the numbness went out of them. Then he could build another fire.
he wanted to kill his husky dog for warmth so he can keep himself alive but when he tackling the dog he realizes that he has no wayof killing it without hands