You're right ... and even more important, if a girl and her mother are treated well by her father, she's not going to be open to radical feminist propaganda.
What does “treated well” mean? There are tons of little princesses out there who have been “treated well” by their parents, they are no less prone to this behavior than anyone else (well, except the those from truly dysfunctional families.) The princesses just have the resources to mask the problems but they get divorced and fall prey to the mass culture soft-feminism that prevails in the media and the Anglosphere.
“Treating them well” only creates a conflict between expectations and reality (as well as their own impulses for a strong figure who will hold them accountable vs. people attempting to ‘treat them well’ as a way to their heart.)
I’d say “raising them correctly” is more what you mean, for you can treat someone well but not raise them right. Raising a daughter (or son) correctly is a tougher matter and may mean you don’t treat either like a prince or princess.
In any case, there are plenty of girls and boys who’ve been ‘treated well’ and are just as messed up and just as much a part of the society which needs to be reformed.