Joseph, your sources are incomplete. You quoted R’ Eliezer’s opinion from Sotah, but left out Ben Azzai’s. Ben Azzai states that a man is required to teach his daughter Torah She’Baal Peh.
The issue is not as clear-cut as you make it out to be. Even the Rambam, who seems to deal harshly with women who learn Torah She’Baal Peh, states that they will receive a reward for their learning (albeit less than a man’s reward.) Where do you ever see someone receive a reward for something that is prohibited? That is completely counter-intuitive, and the only logical answer is that the Rambam did not issue an actual prohibition. In fact, the Perisha suggests that the Rambam was against women being taught Torah She’Baal Peh by their fathers, not women learning it independently. (This is in the majority of cases- the Perisha states that tiflut does not apply for a grown woman who has demonstrated herself to be more grounded than most women. Such a serious-minded woman who deviates from the “rov hanashim” to which Rambam refers may be taught Torah She’Baal Peh even by her father.)
R’ Mayer Twersky concurs, stating that in the case of women who learn Torah She’Baal Peh from their fathers, a problem arises because the Torah is “imposed upon women. Study which is not self-initiated is especially vulnerable to inadvertent distortion and frivolous trivialization.” It is exactly this type of “frivolous trivialization” to which the Rambam objects, and R’ Twersky suggests that self-initiated study does away with the problem. (Also note that the Rambam makes no mention of prohibiting women to be taught by men who are not their fathers.)
This view is also consistent with the Talmud Yerushalmi, which states (Ketuvot 2:10) that one should not teach Torah to a slave, but he is permitted to learn on his own. (Women are often grouped with slaves and minors in halachic matters.) In Succah 2:1, we see that the slave Tavi was even allowed to sit underneath the table in the succah and listen to the Sages discussing Torah. Therefore, women may be present while men learn and can absorb material in this passive way.
The Sefer Ma’ayan Ganim makes an important distinction about the sugya in Sotah:
“What was said in Sotah 20a, ‘anyone who teaches his daughter Torah is as if he has taught her tiflut’, perhaps applied when the father taught her when she was a child…However, women whose hearts prompt them to approach the labor of Hashem through conscious choice of the good- it is incumbent on the scholars of their generation to praise and cherish them, to organize and strengthen them.”
Also, see Nedarim 35b, where the case is given of a man who has sworn not to receive benefit from another. This “other” is forbidden to teach him Torah, as this would constitute benefit, but is permitted to teach Torah to his sons and daughters.
Finally, let’s look at the Rambam’s wording. “Tzivu hachachamim,” he writes- the Sages commanded. Everywhere in the Mishneh Torah where this wording is used, it does not constitute an actual issur v’heter, but connotes a general exhortation of what the Rambam believes to be desirable behavior. Never in the Rambam’s writing does “tzivu hachachamim” precede an actual statement of halacha. (Also note that R’ Eliezer’s wording does not constitute an actual prohibition either!)
Even if you hold by the opinions that do prohibit women from learning Torah She’Baal Peh, the Talmud may not fall into this category. The Rosh rules that it is a positive commandment to write Sifrei Torah as well as Mishnah, Gemara, and books of Rashi commentary. (There is disagreement on whether or not this still applies to Sifrei Torah- but all agree that it applies to the other books.) How can this be so, since it says in Gittin 60b that it is forbidden to transcribe the oral tradition? It must be that when the Talmud was written down, it acquired the status of Torah She’Bichtav and ceased to exist as Torah She’Baal Peh. Therefore, men who teach their daughters Talmud are not teaching them tiflut.