Your "third reason" is simply a restatement of the first. 'Cause you said so? At least demonstrate that.
Actually, it is a different notion: I spoke of what is good for parents in their old age, not the welfare of the children.
Er, no. You are drawing the distinction between the second item on the original list (projected living standard of the children) and the first item on the original list (projected survival of children when parents are old and in need of support). Your "third item" is a restatement of the latter.