I don't think I explained very well, so I'll try again.
I would be very happy if people stopped trying to make things a competition. However, at any point in which people might want to try to make it a competition, we recognize an inherent inequality.
Some of these inequalities cannot be helped. Some people are just more beautiful, smarter or stronger. I'm very against a Harrison Bergeron situation.
When they fall into gender stereotypes, though, we have more of a problem. (Race also, but it's easy to extrapolate and I don't want to fall off track.)
Regardless, though, a balance forms while inequality exists. The rich give money to the poor in the way of charities. Beautiful people help their ugly friends find dates via blind dates. Strong people do heavy and forceful things for weak people.
First wave feminism fought against even these forms of balance. Women made less money, yet they still insisted on paying for half the date. It's counter-intuitive, but by turning it into equality and not a competition, it stopped being culturally acceptable to pay women less for the same work.
Sometimes that balance works in an unexpected way. First wave feminism also fought against holding doors open for women, but now courteous people hold doors open for everyone. People of any sex would rather have doors held open for them than not.
We often expect to find balance by propping up one side we consider to be inferior, but life really doesn't work that way. We cannot simply add to one class of people and detract from another and expect things to balance out, and attempting to do so merely perpetuates the stereotypes and ensures that equality remains out of grasp.
Inequality must be addressed equally.