It may be argued, that if people own themselves, and therefore their liberty and the products of liberty, that creating a child would be the property of the parents. This would mean the parents have all the child's rights.
This makes sense except, the child has an inalienable right to its body, which is also the source of the parents rights. Therefore the baby has rights.
The child does have a natural right to their liberty, but no legal right to their liberty. The parents are custodians of the child because,
These elements are not just specific to children, anyone with mental impairment because of age or genes or chemical imbalances will also fit into the legal custody category. They have legally diminished responsibility for themselves and others, and in return have less legal rights.
A child is not a right, A child is a responsibility.