The best answer to this question is that Guy Montag is the one who had firemen as relatives. We are told this during one of his conversations with his wife.
At one point, Guy is talking to Millie about the death of the old woman. He is deeply troubled by her death and he says that her death is going to stay with him for a long time, like a burned house that smolders for days after the fire is out.
At that point, Millie tells him that he should have thought about that before he became a fireman. He tells her in return that he had no real choice in the matter. His father and grandfather had been firemen and he was simply following automatically in their footsteps.