When the unbalance occurs it would be good to have a dialog between differences. There is nothing wrong with competition as long as one can listen and talk, open and close eye or mouth or doors. For mutual understanding beside not to much monologues there is another important fact: if you don't share the information with your mates or co-workers or Budha-Dharma travelers, you can jump in the wrong conclusions.
And if you don't tell the woman that you dislike eggs or lemons or corn, she can try wery hard to make a delicious meal but it will be of no taste for someone with different preferences.
The same with gender balance. To respect means knowing divine pride and try to understand fallings on knee of the others. Compassion between all living beings for me is not to harm, try to understand first and react next but I agree, when degeneration is in question the reactions are stronger. Maybe in woman stronger than in a men because of helpless wish to protect (rather then nurish after the damage is done).
In my small "The Buddha" book is written: Central to the doctrine are the Four Noble Truths, though the teaching of Buddhism has never been rigid...
That made me to continue despite the silence of the clouds. In basics there is no difference between man and woman, lay or ordained, the light is made for travel the fastest way; we measure the distance (ie. time and space) with the light.
If we can reflect rays to the dearest, a lot of balance is sustained. Between the genders also, do you agree?