One of my favorite Midrashim is the comment in this week's parsha on כֹּ֤ה תֹאמַר֙ לְבֵ֣ית יַעֲקֹ֔ב וְתַגֵּ֖יד לִבְנֵ֥י יִשְׂרָאֵֽל׃. The Midrash writes:
אָמַר רַבִּי תַּחְלִיפָא דְּקֵיסָרִין, אָמַר הַקָּדוֹשׁ בָּרוּךְ הוּא כְּשֶׁבָּרָאתִי אֶת הָעוֹלָם, לֹא צִוִּיתִי אֶלָּא לְאָדָם הָרִאשׁוֹן, וְאַחַר כָּךְ נִצְטַוֵּית חַוָּה וְעָבְרָה וְקִלְקְלָה אֶת הָעוֹלָם, עַכְשָׁיו אִם אֵינִי קוֹרֵא לַנָּשִׁים תְּחִלָּה, הֵן מְבַטְּלוֹת אֶת הַתּוֹרָה, לְכָךְ נֶאֱמַר: כֹּה תֹאמַר לְבֵית יַעֲקֹב
The pasuk places "Beis Yaakov," the women, before "Bnei Yisrael," the men, because in Gan Eden when G-d gave the commandment not to eat the eitz ha'daas to Adam and he relayed it to Chavah, things did not work out so well. This time around, G-d decided to loop in Chavah first.
Whatever the deeper lesson of the Midrash here is, we should not lose sight of the plain meaning of what Chazal are saying. Just because a husband or a father, the "Adam" of the family, goes to daf yomi every day, does not by osmosis cause Torah to pass on to his wife and family. Gone are the days when just being raised in a frum home was enough to ensure that one was knowledgeable in hil shabbos, in kashrus, etc. Chavah -- our wives, mothers, daughters -- need to hear the dvar Hashem directly, to know and study halacha and mussar and other areas, or we risk spiritual churban. Those who misquote the Iggeres haGR"A and say tzinuyus for a women is what Torah study is for a man are mistaken -- it is not. Tzniyus does not give one insight into what Hashem asks of us and wants to teach us. Only Torah study does that.
Going beyond the plain meaning, what Chazal I think are trying to tell us is that Torah cannot be studied via a kli sheni, so to speak. G-d teaches Adam, Adam then teaches Chavah, and along the way in the game of telephone the message is lost. You need to study text first hand. There is no substitute for direct engagement with original sources. The Maharasha was critical of the Shulchan Aruch being published because he thought it would become a substitute for study of the sugyos and Rishonim. One can only tremble at what he would say in our time when ha'levay people would even open the Shulchan Aruch and not rely on other secondary and tertiary sources.
Later in the parsha we read:
אַתֶּ֣ם רְאִיתֶ֔ם כִּ֚י מִן־הַשָּׁמַ֔יִם דִּבַּ֖רְתִּי עִמָּכֶֽם׃
לֹ֥א תַעֲשׂ֖וּן אִתִּ֑י אֱלֹ֤הֵי כֶ֙סֶף֙ וֵאלֹהֵ֣י זָהָ֔ב לֹ֥א תַעֲשׂ֖וּ לָכֶֽם
Unlike Ramban who learns that the latter pasuk prohibits avodah zarah b'shutfus (meaning there is some power in addition to G-d that controls things) , Netziv (based on Seforno) learns that it prohibits the worship of Hashem via an intermediary (meaning G-d is the only power, but He can be approached through some intervening medium). Hashem tells Bnei Yisrael that He spoke with them directly at Sinai -- He did not communicate through an intermediary. So too, when we speak to Hashem, when we study the dvar Hashem, it should be done directly, not through intermediaries. Everyone has a direct connection.