This is what we may refer to as the "Yeshiva World" view. This is from the work called the Maznayim l'Mishpat by R' Zalman Sorotzkin. This was written in 1941 when he was in Israel.
In answering the question, he writes to the questioner that his idea about women- their learning the Oral Law if they are really smart and excel and the Written Law for all- most of what this questioner writes is very good. The only thing we have to worry about is learning the Oral Law in depth. Now, in Bais Yaakov they learn the Written Law, which is no problem, and the Oral Law they learn, they don't learn in depth. So he defines the problem, in terms of what could potentially cause tiflus, meaning that learning the Oral Law in depth, and pilpul- that is what is forbidden for women; that's what's considered tiflus. He thinks the halakha is straight and clear- the Written Torah is fine, the Oral Torah is fine, it's only the Oral Torah in depth that can cause problems.
And in his work "The Dei'ah and the Diybur" he says that in the Oral Law woman can also learn the conclusions, because you have to know what it says in the Torah and what to do! So why do people get so upset about women learning Torah? Only because it's something new- they never saw their forefathers do this. Now, from experience and watching you could learn the whole Torah, so you might as well teach them from the sefer. He compares women here to a non-Jewish woman who is going to convert- you have to teach her the Torah, she never saw it before but now you teach! So he's saying, if you had a girl who was coming to convert you'd teach her, how much more so the Jewish girl.
The Maharsha quotes Rashi and says that women knew how to pasken on halakhos. But that's difficult, because how could they learn Torah? So that was because at that time period, King Achaz had closed all the batei midrash (houses of learning) because "if there are no lambs, there are no sheep," meaning that if children don't know Torah, neither will adults. So Chizkiyahu, his son, had to come and redo everything. And because Achaz uprooted faith from the hearts of Bnai Yisrael, Chizkiyahu found it necessary to teach Torah, even to the women. R' Sorotzkin extrapolates from this a kind of risk to benefit ratio- where the benefit of teaching women Torah outweighs the risk, it makes sense to do it.
He quotes a verse from Shir HaShirim (Song of Songs.) And at a time when the non-religious abound, we too have to do what Chizkiyahu did.
This next part is, according to R' Auman, particularly fascinating.
We see by Avraham that we worry about the faith of women more than that of men. Avraham's tent was holy- a place of Torah and learning to bring people close to God. Avraham actually had 2 tents, one for the men and one for the women. He pitched Sarah's tent before his own (represents that you take care of women's learning before taking care of men's learning.) And nowadays, when there's a question of which section in shul you put up first- the ezras nashimn or the ezras anashim- it's obvious, men have the obligation to pray 3 times, women don't have the obligation, so put up the men's section first! Also, there's an obligation to teach your son Torah but not your daughter, and we never heard of the daughter coming first (in terms of a school for girls before a school for boys) but we see by Avraham that the women came first! So when you live in times like Avraham, you do as Avraham did.
And in this way God commanded Moshe by har Sinai, saying:
ג וּמֹשֶׁה עָלָה, אֶל-הָאֱלֹהִים; וַיִּקְרָא אֵלָיו יְהוָה, מִן-הָהָר לֵאמֹר, כֹּה תֹאמַר לְבֵית יַעֲקֹב, וְתַגֵּיד לִבְנֵי יִשְׂרָאֵל.
3 And Moses went up unto God, and the LORD called unto him out of the mountain, saying: 'Thus shalt thou say to the house of Jacob, and tell the children of Israel:
Chazal says it means- "So shall you say to the house of Jacob," meaning the women, and only then do we mention the men.
(THIS IS WHERE I AM UP TO IN CLASS, SO THIS WILL BE CONTINUED)