This shiur is a case study in how a psak acts to set communal policy, focusing on the issue of women’s learning. The shiur and sources are available: here.
The Rav wrote two letters when asked whether girls should be taught Gemara. The second, which is much more famous, affirms that we should open the halls of תורה שבעל פה to women. However, in the first letter, which I think is critical to understanding the letter, first requests assurance that his answer will be accepted as binding. Here, it is worth remembering that asking for psak is different than asking for Halachic advice, and for reasons that I have discussed elsewhere, psak obligates the asker of the question to accept the conclusion. Thus, it is clear that the Rav did not just want to inform people of his opinion, he wanted to set policy. In the substantive letter, the Rav does not provide sources, though promising to provide them in a later letter, which seems never to have been written. The effect of the letter, I believe is to make the question one that is not subject to debate. For the community the Rav wants to create, this is not an open question.
R. Moshe Feinstein has a teshuvah that is in many ways similar. It was posed by R. Elya Svei, the Rosh Yeshiva of Yeshiva of Philadelphia. This too was a teshuvah meant to set policy. R. Moshe asserts that it is assur, but does not provide his sources , because it is “so obvious.” Here too, the teshuvah is not up for debate.
As to what drove both arguments, I can only speculate. For R. Moshe, it seems to be that the Gemara (and this is nifsak in Rambam and Shulchan Aruch) claims that teaching one’s daughter Torah is like teaching her tiflut, which either means vanity or licentiousness. The Poskim distinguish between Torah BeBichtav and Torah SheBeal Peh, the latter being tiflut and the former just assur.
However, while at first glance this seems to close the discussion, R. Moshe’s argument is weak. He does not argue, nor do most people post Chafetz Chaim, that women cannot learn Tanach. However, this is also prohibited, it is just not tiflut. Thus, unless one claims an eit laasot which we minimize as much as possible, it seems that people do not understand the issur to be absolute. This is bolstered by the Shulchan Aruch’s claim that only most women would be led to tiflut, implying that if there are women who, let’s say, are educated and know how to deal with the material it would be mutar. The Prisha adds that women who choose to learn can, it is only a problem if the teacher initiates and teaches. Thus, it would seem that when women are educated and can deal with the material, and as the Chafetz Chaim noted, we have no choice but to give them a sophisticated vision of Judaism through Torah, that Torah SheBeal Peh should not be fundamentally different. Add to that the fact that Talmud Torah is necessary for Ahavat HaShem (ala Rambam) and that was the Chafetz Chaim’s goal, it should follow that Gemara is mutar as well. While Yeshivish poskim deny this, it seems to be the logical conclusion of the path set by Chafetz Chaim, or at least a likely one.