[F]irst, that a man should harm no one, and second, that he should do good to all, so far as he can. In the first place, therefore, he must care for his own household; for the order of nature and of human society itself gives him readier access to them, and greater opportunity of caring for them." City of God 19.14I agree with Augustine. There is an order of caring. One is to care about one's neighbors' children, but one is to care for them only if one's own children are appropriately cared about and cared for. But in addition to having readier access and opportunity, one's children belong to one's family. My children belong to me as their father--not in the sense of property ownership but as a gift ultimately from God. God has given my wife and I the responsibility to care for these gifts.
Suppose I don't think of my children as a gift from God. It might be natural, then, to think of them as wholly the creation of my wife and me. Is there a non-theistic reason--beyond prudential reasons--for not selling my children after they were born?
I'm unsure, but the only plausible reason I can see at the moment is that the baby becomes attached to the mother and might undergo stress from maternal detachment (perhaps some additional stress too from no longer hearing the voice of the father). But if one were to run a utility calculus, and the mother and father did not want the child and felt burdened by it or by poor finances, it's hard to see why selling one's small children is unjustified.