Your concept of a large family as inherently misogynistic is completely incorrect. It has no factual basis. Did you base the claim off a study found somewhere? I'm curious, mostly because I'm sure I could find many an article to counter it with.
I know a variety of large families (as well as small and medium) and the number of children involved is irrelevant to the beliefs taught within the household. Actually, the few girls I know who have ended up in relationships that are borderline abusive (or mutually abusive, in one instance) came from families where they were either the only child or one of three. They didn't receive much emotional support or attention from their parents growing up (one had an absentee father) nor were they pushed to take education seriously - perhaps these factors contributed to where they are now. I don't know. Every case is different. But it obviously was not a product of a large family.
On the other hand, both my parents came from families of 5 (Mom) or 6 (Dad). None of the men became abusers, none of the women suffer(ed) from low self-esteem or were ever abused. In fact, in my mother's childhood home the concept of women learning to stand on their own and become capable of tasks men might traditionally do, as well as always standing up for themselves, was actively focused on and encouraged.