Without a clear story of the apocalypse that was clearly of the nuclear variety, McCarthy leaves open the possibility that there was no real good-guy bad-guy type of conflict. Along with so much of the novel, the suggestion of the darkness and depravity that exist in the depths of all humanity is an important theme that is maintained by the omission of the reasons for or the exact progression that led to this horribly mangled world.
Particularly as the man and his son progress along their journey, the fear that there are simply no good people besides these two, the torn and half-broken man and his innocent and wide-eyed son, is a very real one. This fear helps to drive the action of the novel and would likely be less overwhelming if there had been any explanation of how the world ended up this way. The lack of any sort of explanation of how the world got this way serves in part to create the sense that it has always been this way and makes even more powerful the hopelessness that pervades so much of the story.
I do not think there is a right answer to this question, but I'll answer according to what I thought when I read the book.
I think that McCarthy did not reveal what made the setting of the story as post-apocalyptic as it was because it was intentional. By doing this, it gives a sense of mystery and the fear of the unknown. In books where everything is elaborated, the reader do not feel these things. If you think about it, if McCarthy told us exactly how the world ended, we would know what to expect in the book. As an example, if the world ended in a zombie apocalypse, we would know to expect them to be wary of wandering zombies. Since he did not tell us how the world ended, it leaves us craving for more as we grow a desire to uncover the secrets of the setting.
In a shortened and more simplified manner, McCarthy omitted this piece of information to create an uncertain vibe for the reader. The story gains an utterly terrifying atmosphere.
If you wanted to know what else the story gained from this, well, my answer to the first question seems to have answered the second as well.
I hope I've helped! Good luck with literature.