On page 75, the man says: "please don't tell me how the story ends." What is he referring to and why does he not want to know how it ends?

The man says this early on in the book. There is always the presence of the existential. The father knows they are relics in a dead world. The vestiges of humanity that are left are evil: perhaps the true nature of man. The man fears that he will have to kill his son at the end of this story to spare him even a worse death. At least for that moment, the father does not want to think of the end of their narrative.