Here is the beginning of that particular chapter:
We have
now established each man's property right in his own person and in the virgin land that he finds and transforms by his labor, and we have shown that from these two principles we can deduce the entire structure of property rights in all types of goods. These include the goods which he acquires in exchange or as a result of a voluntary gift or bequest.
There remains, however, the difficult case of children. The right of self-ownership by each man has been established for adults, for natural self-owners who must use their minds to select and pursue their ends. On the other hand, it is clear that a newborn babe is in no natural sense an existing self-owner, but rather a potential self-owner.[1] But this poses a difficult problem: for when, or in what way, does a growing child acquire his natural right to liberty and self-ownership? Gradually, or all at once? At what age? And what criteria do we set forth for this shift or transition?...
Even from birth, the parental ownership is not absolute but of a "trustee" or guardianship kind. In short, every baby as soon as it is born and is therefore no longer contained within his mother's body possesses the right of self-ownership by virtue of being a separate entity and a potential adult. It must therefore be illegal and a violation of the child's rights for a parent to aggress against his person by mutilating, torturing, murdering him, etc. On the other hand, the very concept of "rights" is a "negative" one, demarcating the areas of a person's action that no man may properly interfere with. No man can therefore have a "right" to compel someone to do a positive act, for in that case the compulsion violates the right of person or property of the individual being coerced. Thus, we may say that a man has a right to his property (i.e., a right not to have his property invaded), but we cannot say that anyone has a "right" to a "living wage," for that would mean that someone would be coerced into providing him with such a wage, and that would violate the property rights of the people being coerced. As a corollary this means that, in the free society, no man may be saddled with the legal obligation to do anything for another, since that would invade the former's rights; the only legal obligation one man has to another is to respect the other man's rights.
Applying our theory to parents and children, this means that a parent does not have the right to aggress against his children, but also that the parent should not have a legal obligation to feed, clothe, or educate his children, since such obligations would entail positive acts coerced upon the parent and depriving the parent of his rights. The parent therefore may not murder or mutilate his child, and the law properly outlaws a parent from doing so. But the parent should have the legal right not to feed the child, i.e., to allow it to die.[2] The law, therefore, may not properly compel the parent to feed a child or to keep it alive.[3] (Again, whether or not a parent has a moral rather than a legally enforceable obligation to keep his child alive is a completely separate question.) This rule allows us to solve such vexing questions as: should a parent have the right to allow a deformed baby to die (e.g., by not feeding it)?[4] The answer is of course yes, following a fortiori from the larger right to allow any baby, whether deformed or not, to die. (Though, as we shall see below, in a libertarian society the existence of a free baby market will bring such "neglect" down to a minimum.)