The libertarian philosophy (essentially the non-aggression principle) has been regarded as having weak arguments against (ironically) aggression against one's own child or one's own pet.
After all, if property rights are everything then certainly I have the right to torture my cow just as soon as eat it, right?
Here I feel we must take a more holistic view of the topic. Lets consider the non-aggression principle, Property rights in the light of the principle of Contracts.
When one has birthed a child or bought a kitten one has literally assumed responsibilities not to let that living entity to come to harm. If it were not a living entity (or should we be more specific; a conscious entity capable of feeling pain and fearing death), if it were a hammer for instance it's owner could melt it down, burn the handle and spread the ashes over the sea. The fact that it is capable of experience means it falls under the purview of the non-aggression principle.
This assumed responsibility to care for this entity is essentially an informal contract with the entity not to let it come to harm (that is not to say, "not to let it feel pain," for some pain may be highly useful to its continued existence and happiness).
Therefore if one abuses their child one has not only violated the non-aggression principle by definition, but one has also violated an informal contract he has with the child (and anyone who cares about the child).
Besides that one cannot "own" a child, one can only be responsible for a child. Children do not come with property rights, you freely choose to create them and therefore are automatically endowed with the responsibility to care for them.
Let us lastly consider again my cow. Cows only exist to serve humans. They've been domesticated and bred that way. That is to say if we didn't exist neither would the modern cow. This is not an argument to say this is why cows can be property and babies cannot, it is a note on our relationship between the two species. The cow obviously has a lower intelligence, but maybe not a lower ability to feel pain. Therefore is its commensurate to raise, feed, care for, and butcher cows, (we all must work for a living), but it is not fair to torture them. That is a violation of the non-aggression principle.
