Learning Torah is the most important act a Jew can do.
The Mishna in Sotah states that teaching one's Daughter Torah is the same as teaching her Tiflus. Nobody is sure exactly what Tiflus is but it is pretty much agreed that it is a negative thing to do. But, aside from the legalistic definitions and distinctions made by Poskim, I believe that ...IF... anything at all is Assur, it is a man teaching a woman. And then it would only be certain areas of Gemarah, certainly not all Gemarah. And even that is arguable. And if I understand correctly Rabbi Joseph B. Soloveitchik believes that it is entirely permissible to teach Gemarah to women today. But other Poskim disagree with him.
None-the-less, certainly a woman learning from other women or on her own should not be Assur at all on any subject including all of Mikra, Mishna, or Gemarah. In cases of exceptional bright and motivated women, no one should object to a man teaching Gemarah to a woman.
In Judaism, roles for men and women are clearly defined. The Gemarah speaks about women saying that Kvodah, Bas Melech Pnima, which loosely means that the glory of a woman is in the home setting. But, the issue of women learning Torah should have nothing to do with what a woman's role in Judaism is. On this issue, the only thing the Torah does is define where priorities lie in the roles of both. Men are required to learn as much as they can: VeHagisa Ba Yomim VaLaila. Women are not. They are Aino Metzuveh VeOseh. This means they are not required to learn as are men, but they may learn if they choose to. As such, they should be provided every opportunity and every resource.
Historically it was considered quite radical for women to learn Torah at any level and certainly not at levels usually reserved for serious Bnei Torah. There are some famous exceptions of this such as the Tanna Rebbi Meir’s wife Bruriah, and much later in history the “Maid of Ludimir”. But these were the exceptions that proved the rule. In both cases their fate was less than ideal. Beruriah committed suicide and the “Maid of Ludimar” never got married and taught Torah from behind a Mechitza, hardly a normal situation. So if history is a lesson for us, why allow women so radical a change? The following bit of history should illustrate.
Before Sara Shneirer founded the Beis Yaakov movement, women studied little more than the Halachos their everyday lives required as both Jews and women. Young girls usually married quite early (often in their teens ...as young as 15 or 16) and would stay home and learn how to be a Jewish woman from their role model mothers. It was also beleived that women should refrain from formal Torah study as this was the province of men who are commanded to do so. Spending time on activities that would detract from learning that discipline was thought to be wasteful. But with the advent of enlightenment and the opening up of universities to Jews a lot of women were attracted and thereby in danger of leaving Yiddishkeit because of the anti religious atmosphere of academia, a condition that persists to this day.
So, no less a figure than Rabbi Yisrael Meir Kagan, the Chafetz Chaim, proclaimed a Hora’as Shah... an Eis La’asos... a time to act. The time had come to abandon the traditional modus operandi of women’s education (or better... lack of it) which was based on the concept that teaching women Torah was the same as teaching them Tiflus. In essence it was felt that women who were drawn to use their minds beyond the basics of Yiddishkeit in the home should be given a venue to study Torah in a more formal way rather then be exposed to the values taught in universities to which they would otherwise be drawn. Going to those universities without any real Torah Hashkafa preparation outside the home would have had disastrous consequences. This being the scenario, the best and brightest of our daughters, the future mothers of our children, would have abandoned Judaism wholesale.
This brings me back to the present. From this little piece of history it can be seen that it is justifiable to allow women to study all manner of Torah study, should they choose to do so. The mind is a terrible thing to waste. But there is a caveat.
A feminist Agenda should not be the cause for such learning and there are some feminists who learn for precisely that reason. Should that be the sole cause of study, I would be against it. But I believe that any serious student of any gender should not be banned from this field of study. The positive benefits of serious Torah study outweigh the negative debits of the insincere motivation of some.
Frankly it is inexplicable to me that, today, anyone who has any kind of brain should be forbidden to delve into even the greatest intricacies of Torah study. As long as one fulfills their destiny as a man or a woman one should be able to use discretionary time in the way which he or she understands is the best use of that time. If a woman loves learning a piece of Brisker Torah, what possible harm could there be? Why should a woman be denied the joy of understanding a R. Chaim? Or being able to be Mechadesh her own Torah?
The answer is: There is none.