Parents have no absolute right to rear their children as they wish. Their right is limited by the rights/desires of the child.
Obviously this theory is untrue at age four. So when does it become true?
Supposing it to be true, is such a right likely to be respected in an anarchic society?
In an anarchic society, people without income, assets, or reputation, are likely to receive a lesser level of protection. Also, most people will be inclined to view that a parent punishing his child is probably doing it for the child's own good, and are likely to be disinclined to protect a child against his own parents.
Protection, the application of organized force, will be mediated through the adult income earning members of the family, and to the extent that force is applied by the individuals directly concerned, the male members of the family, thus whatever you believe
should be the case, an anarchic society is likely to have greater parental and patriarchal authority than a state society, hence will tend to be socially conservative in family matters, regardless of what anyone thinks it should be.
No welfare payments for single mums, no free childminding and brainwashing services, weak limits on patriarchal use of force, therefore socially conservative. Fathers are likely to use violence to ensure that their daughters and those courting their daughters behave in a manner likely to ensure support for their grandchildren. Such violence is likely to be socially acceptable because widely applied, and because no one with means to prevent it has any individual interest to prevent it.
In an anarchic society, whatever use of force is common and normal and people generally get away with it becomes legal, or not illegal, and whatever acts are apt to result in violence being successfully used against one, become illegal. Patriarchy, therefore, is apt to be legal. Whatever laws should be in theory, in practice they are apt to be biased in favor of those doing the enforcing.
Analogously, i