Two reasons are stated: One is when people think they need to have a lot of kids for any of them to survive. "Them" is children, not parents.
The other is when human beings think their children will have it better than they do. Again, this is about children, not parent.
Which is why I mentioned childbearing as self-protection on the part of the parents. The focus here is on the parents' survival and welfare. Wouldn't you say that this point is independent of the two? Not to belabor the issie, of course.
No. The reason for parents to have enough children to guarantee that a few survive, in an environment where mortality is high, is to provide themselves with old-age insurance. That's why your "third" point is simply a restatement of the original first point.