Earlier quoted context omitted.
> What I really want, is women to show they can overpower a society of competitive values (which is typically male), with more values of mutual help, and I mean this in the political realm, as in socialism and a society made of collectives, not a society made of owners. Wouldn't "overpowering" those "competitive values" be using a competitive mindset and sabotage the effort for "values of mutual help"?
the competitive mindset pits every individual against every other individual. this is different from a group of people combining their forces to push out an unwanted trait.
Both cooperation and competition is part of the human psyche, and there is a place for competition as well (such as the refinement of personal character and development of capabilities). More problematically are such things as, exploitation, rent-seeking, status-seeking, etc. There are also problems when people in cooperation are not mature or capable enough to take care of themselves and cannot then adequately contribute, and others who contribute to the point of undermining their own health and development.