As for the beginning of that paragraph -- the Gemara itself says that women are not supposed to be taught Torah sheba'al peh.Oh, how moronic, and on so many many levels. Permit me to elaborate.
I think that anyone who says that that Gemara is not Torah miSinai - but is only a response to the surrounding culture of its time - has herself been influenced by the "surrounding non-Jewish influence" of /our/ time.
There have been very learned woman, but in each case -- be it Devorah or Bruriah -- she was very much an exception to the general run of Jewish women. How many female shoftim have there been? One. How many female tannaim? One. (If Bruriah counts.)
So while there does seem to be an allowance made for the exceptional circumstance, it is not the norm for women to be talmidei chachamim. Their exemption from the mitzva of limud Torah (except for the specific halachos they need to know) is, BTW, related to their exemption from other mitzvos that would interfere with their higher duties -- raising the next generation of Jews. --- A WOMAN WHO TEACHES SCHOOL
1 - There are Rishonim who wrote that the much of what we call the Gemara isn't "from Sinai." Logic suggests this as well. (After all, could every "Rabbi Yehuda amar" have been spoken at Sinai? Imagine what a hoot it would have been for Rabbi Yehuda to learn in school what his older self had been pre-destined to say.)
2 - Why does past performance predict future results? In the old days many forces conspired to produce few learned women. Those forces were not inherent to Judaism, and, happily, they have, for the most part, passed into oblivion. So why should women sell themselves short? Out of sentiment? Out of nostalgia for forces that no longer obtain?
3 - "The halachos they need to know?" That could fill a library, (not to mention much of Nashim.) So where are the schools committed to teaching women these laws, in all their detail?
4 - Anyway, it is not "the Gemara" that says what she's referring to. It's ben Azzai (I think), as quoted in the Gemara, and he only states one opinion amongst three. "The Gemara" does not take sides between the three opinions. But for some reason (hmmm what oh what could it be?) the "tiflus" opinion is the one that's become famous.
5 - Besides, how does this "woman who teaches school" know about Bruriah? Heavens. Did someone teach her Talmud?