(Material by Rabbi Kenneth Auman, presented by Chana. All mistakes are my fault.)
Please look at the Tur page, which states that there is a general rule that one who does something he is commanded to do receives more reward than one who does something he is not commanded to do. Even though a woman is granted reward for learning Torah, still one shouldn't teach his daughter Torah because most women have very poor intellects. (He misquotes the Rambam here- it should be the reverse.)
Now look at the Perisha- it's talking about women who knew Torah and Gemara- if a woman is able to learn well, that's fine and good. But the father still is not supposed to teach her because he doesn't know what she's thinking at the time (and how she will use or misuse what he teaches her), but if she learns Torah on her own, that's fine.
(So we ask a question- how can anyone learn if one's father won't teach her? So it seems that the deal is that it's forbidden to force the women to learn, but if she shows interest, that's fine. So it apears that the Derisha feels the problem is only when the woman is forced to learn. Rambam says "rov nashim" are not supposed to learn but if a woman is an exception to the rule, it's fine to teach her. Derisha advocates for voluntary learning.)
Next question is where does this division between Torah she'Bichtav (the Written Torah) and Torah she'ba'al Peh (the Oral Torah) come from? The Rambam made it. Where did he get it from? So the Bach (Bais Chadash) discusses this.
There is a mitzva of Hakhel (where the king read from the Torah to the assembled people of Israel- men, women and children.) Now, the men are coming to learn. The women are coming to listen. The little children come, even though they don't necessarily understand what is happening, so that their parents receive merit for bringing them.
Anyway, clearly women have to hear the Written Torah at Hakhel, so this is where the Rambam derives this from (regarding the division he makes between the Written Torah and the Oral Torah, as opposed to putting them in the same category.) Now the same Rabbi Eliezer who says that women must hear the Torah by hakhel is the one who says that teaching women Torah is like teaching them tiflus, obscenity or foolishness. So against your will you have to say that Rabbi Eliezer believes that you can't teach your daughter the Oral Torah, because obviously he believes that women do hear and understand the Written Torah at hakhel (where it was even translated into Aramaic for them.)
Now the problem with this interpretaion is that the Tur and the Rambam say women shouldn't even learn the Written Torah. So the Bach goes on to say that men came to learn while women came merely to hear. The different words (learn vs. hear) show the distinction, so women should avoid the Written Torah as well- that's where Rambam got it from.
Now look at the Shulchan Aruch page.
Look at daled in the Taz.
He fixes the misquotation of the Rambam, then talks about hakhel- learning Torah is permitted for women like it is permitted in that context, where it is the mere translation, it is simple. Women, indeed, have always learned Torah. But for women to learn deep Torah with commentaries- that's already an issue. That's why the Talmud says that women are merely supposed to hear (l'shmoa)- for women to learn Chumash simply is fine, but they should not learn deep explanations or pilpul. The Rambam is onloy forbidding women from learning deep explanations of Chumash.
The Taz is therefore saying there's really 3 levels that we are dealing with:
1. The Written Torah (Torah she'Bichsav) - which is permitted l'chatchila
2. The Written Torah in depth (with commentaries)- which is permitted b'dieved
3. The Oral Torah - which is considered tiflus/ not permitted