I haven’t read through this entire thread but it seems to me that there is confusion going on between the klal and the yachid.
Many, many, mamarei chazal apply to the rov, the majority of the population. It does not mean that there are no exceptions or even that exceptions are exceedingly rare. Furthermore, circumstances can change such that exceptions will become more common.
Now I think that in general women and men are quite different and suited for different roles in a frum society and in society in general. But that does not mean that individual men and individual women cannot be exceptions to that general principle and be suited for a role that is typically for the opposite gender. So although the average woman is not suited for learning Gemara (and I acknowledge the possibility that this has changed), an individual woman who has a cheshek to learn can and should learn Gemara and shteig. And although the average man is suited for learning gemara, an individual man might be ill-suited and, upon discoverying that fact, should spend his time learning and doing other things.
I have never been in a Bais Yakov, and I don’t really know how things are taught there. I suspect that different girls going through the system fixate on different things that are said and different messages that are being sent. Thus even if some level of nuance is inserted into the Bais Yakov message about motherhood being the foundation of klal yisroel (an undoubtably true statement), it might very well get lost in the transmission.