I hate to act like a curmudgeon, but it is written:
“Let women keep silence in the churches, for is not permitted for them to speak, but to be subject, as the law says; but, if they would learn anything, let them ask their husbands at home, for it is a shame for a woman to speak in the church.”
1 Corinthians 14:34-35.
If St. Paul was a sexist and misogynist, then I guess God (who spoke through him) is a sexist and misogynist. “Let all mortal flesh keep silence”, it is true, but let women keep a greater silence in Church out of respect for the vices of their gender. Men have particular vices easily manifested in us (most often choleric in nature) which must be conquered, and women have particular vices easily manifested in them (most often sanguine in nature) which must be conquered! Whereas men are more often sinful by concupiscence (food and sex drive), women are more often sinful by irascibility (emotional drive). Quarreling is proper to men as a vice, and gossip is more proper to women; both are the vice of immodesty, but they’re still different forms of the vice. This is not my opinion, but the experience of all wise people through the centuries.
Common experience tells us that God made human beings differently. We have our strengths and weaknesses. The weaknesses of women are more obvious in communal spaces, and the weaknesses of men more obvious privately. “Men and women He created them”, and nothing less. Women should be subject, quiet, humble, and loving; men should be dominant, strong, bold, and protecting. It is a mutual help, a synthesis!

We are different, not equal.
What can women do? They are certainly not leaders by nature, but nurturers. Women keep the children, the home, and the emotions, while men keep the workplace, fellow men, and logic. Women can, no doubt, be workers, friends, and logical: but these virtues are more proper to the stern mind of men. As childish as we men can be, we are built differently. We are leaders, and women are excellent in what they do. There are various and diverse ways women can “lead” in Church, anyway: by prayer and holy example.