The first on the scene
I have a duty to love and care for these children (namely, mine). Why should that be so? Niko Kolodny helpfully refutes one wild answer, that someone has to do it, and that I—and their mother—are no worse, and possibly better candidates, than any others. In a more formal register, the proposal, which he rejects, says
Society has a collective responsibility to care for those unable to care for themselves, such as the very young.
Moreover,
Shares of this collective responsibility must somehow be assigned to those of us who can fulfill it.
The “somehow,” which “assigns shares of this collective responsibility,” must be some system of laws and social conventions. This system ought to be “fair and efficient.” (“Efficient,” in that it best promotes the well-being of the children, or does so at the least cost.) And in most cases “assigning genetic parents care for their genetic children” meets these conditions. In particular, this policy is efficient,
because typically [genetic parents] are “first on the scene” and strongly motivated to care for their genetic children.
I think that’s a touch of fun, “first on the scene.” Yes, we were first on the scene when our children were born. O happy coincidence! How things might have gone, if someone other than their mother had been first on the scene!
So what is wrong with this idea? Kolodny’s objections are, first, that when I care for my children, I am not moved to do so by the thought that society is collectively responsible for the care of children, and that this is how I do my part. If, therefore, the offered justification were correct, I would be moved to care by the wrong reasons; which I am not. And second, if I learned, years later, that the hospital had mistakenly swapped my child for someone else’s, I would reasonably be upset, want to meet my lost child, and hope that they were well. But none of these would be reasonable, if duties to children were explained as above.
Of course, wide-eyed deontological libertarians aside—reader, I’ve met them, and seen their unwashed hair—society does have a collective duty to care for the helpless, children included. The point is that, once this fact has done what it can, to explain our duties to our children, some raw nerves of feeling and desire remain exposed, and unsupplied with reasons to rationalize them.
The natural alternative is that I have a duty to care for these children because they are mine—they are children that my wife and I created, in the usual way by which this is done. Now philosophy is an endless escalator of why-questions. If indeed that’s why I have a duty to care for my children, it remains to be said why it is that that is why.
Kolodny does not answer this question, but he does speculate. First, he observes that

