The fact that we're equal is not the issue. Men and women have their own spaces, such as private all-girl schools, despite being equal.
Why? Because men and women are equal but different - in physicality and mind.
Men and women learn differently, they mature at different rates, they experience anxiety and phobias at different rates, they focus on things vs people and logic vs emotions differently, they have different rates of exceptionally dull and exceptionally high intelligence, they have vastly different mating strategies and libido, they engage in high risk behaviours at different rates, and on and on.
Setting aside physical capabilities, female spaces exist for good reason.