You make some good points about parental rights.

Look at vaccinations. (Vaccinations are good; I had no hesitation having my child immunised; I'd like schools to require immunisations for pupils; etc). The early days of the vaccination scandal were not presented as a bit of scientific research, it was "you, as a parent, are harming your child by vaccinating them" (and that's still what the nutjobs are saying). Now that we know that Wakefield is a crook we tend not to say "you were duped by a crook who had financial interests in misleading you so let's help you get your child immunised", we say "you're a nutjob and a bad parent".

Look at HN where parents feel guilt about work life balance for one example of how hard it is to be a parent in a rich first world country.

Look at the number of people on HN who (ignoring law) say they would hesitate to employ women because of the risk of maternity leave.

The fact that "having a child" has to be written into legislation as a protected status shows that status of parents was seen as needing protection.