We don’t really know why so many people survived the “apocalypse” in Cormac McCarthy’s The Road. I’m not really sure I would say “so many” survived. The father and son walk for great stretches without encountering anyone. However, it’s true that they are continually on the lookout, knowing that they could wander into a dangerous situation (anything that involves other people) at any time.
The reason we don’t know why so many people survived is because the author never tells us about the nature of the disaster. We simply don’t know what happened. McCarthy wanted us to focus on the aftermath of the disaster, not the cause of it.