This is what people are like: only a minority of people will go through the motions of self examination, and only a minority of those will do that effectively. Where real change happens, or where outdated misbehaviors persist, it's basically a matter of primate see, primate do. Real change has to have a component of motivation at this level.
If women want to compete with men and not just be their toys, they need to exercise agency and own their decisions that "No, I am not up for a relationship with you. Because I say so, not because of some other man's property rights over me." If a woman says "I would get with you if I weren't with someone else" she needs to really and truly mean that. It shouldn't be a polite fiction. Such polite fictions tend to lead to worse trouble than the one they thought they were trying to cleverly sidestep.
I would argue that there is a concept of "relatedness" encoded into Homo sapiens on the instinctive level. The notion of "family" is at least in part a cultural construct on top of that. Also, who said I was arguing against "mine-ness?" I certainly didn't. I'm just highlighting possible unacknowledged/unsupported assumptions in this thread. (Like your apparent assumption of a particular stance on my part.)