And not all Gedolim agreed with the BY movement; the Hungarians objected to the teaching of Rashi to girls (and certinaly Rambans and Maharals) on the claim that that constitutes Torah shebal peh. Others said that since Rashi merely explains the pshuto shel mikrah – the simple meaning of the text, it would be considered Torah shebiksav in this sense.
(IMHO) The Chevra is correct. “Women learning” ended up being a Machlokes between most Chassidim and Rabbi Miller in one corner, and Rav Kotler and most Litvish Rabbonim in the other. (that is an opinion, not fact)
It seemingly stems from the same Machlokes if women should work and men learn, or men work and women stay at home.
SJS: You are correct about the Chiluk between learning and teaching, see the Rambam I quoted.