Exactly, patriarchy is in essence a dominance based hierarchy and girls/women often contribute to maintaining it. Since one of the aspects of this social systm is a dog-eat-dog mentality where if you don't win, you lose, any sign of vulnerability or weakness makes you "the loser." It's a destructive and harmful paradigm all around, even for those at the top of the pecking order because they have had to suppress their humanity in order to get there.