@Olivier5,
It is a mistake to see cooperation as a feminine trait. Successful male dominated teams have been typified with cooperative behavior from NASA to sports teams to the American Congressional Congress in the 18th century.
It is also a mistake to see competitiveness as a masculine trait.
You can not be successful without having competitiveness as a trait; you need to confidently promote ideas, expect to be heard, demand space and resources, take leadership over others, win over other people ... these are all essential traits for success.
Cooperation and competitiveness are not opposites. In a sports team, or an engineering team or a army platoon... individuals are cooperating with each other to reach a goal and at the same time competing with each other individually.
This is another area where I teach my sons and my daughters the same. They should exhibit both the ability to cooperate, and the ability to compete.
They are both valuable skills for anyone.