Why did the father choose to survive and not the mother? What did he see that she could not.

The mother chose to end her life because she didn't feel it was worth living. She doesn't want to watch her family brutalized by the barbarians. She says, "Sooner or later they will catch us and they will kill us. They will rape me. They'll rape him. They are going to rape us and kill us and eat us and you won't face it." The mother chooses her own death; the father chooses to find a future for his son.... a future he still believes in.