Q. How do you answer someone that says religious woman are second class?
A. Religious women are A-1 class. There's nobody better than religious women. Now what about religious men? Also A-1. Certainly. We are not going to say women are better than men. They want to say they are second class compared to religious men? Look. With HaKodesh Baruch Hu there's no such thing. Everybody is judged on his merits. Like I mentioned before, a righteous Torah woman, a woman who is Orthodox, and is loyal to HaKadosh Baruch Hu, and tries her best, can many times outdo the biggest tzadickim.
I gave you one example here, the Rebbetzin Kaplan who made a revolution in America, and she did more than any single Rosh Yeshiva did in America.
But even if you are not such a successful personality, in your own home, if you serve HaKadosh Baruch Hu with a pure heart and you try very hard, there's no question you can become great.
What do you want, you want to hold speeches? Speeches are not for women to hold in public. There's a reason for that. It's a biological reason. Can't be helped. Women can speak to women. But you can't become a Rosh Yeshiva if you are a woman. And don't bewail the fact that you can't become a Rav HaKollel, a chief Rabbi. There's a reason why women cannot do that. It's a technical reason.
Therefore, every person should utilize his opportunities. And women have opportunities to become great no less than anyone.
R' Avigdor Miller, I Created All of Them for You #491 1:13:45