R' Gil inspired this with this post. It lacks a little polish, I apologize; I didn't have enough time to properly finish it.
I once gave a drasha in honor of my Bubbie, and part of it was this: Kiddushin 49b says that 10 measures of yofi came to the world and Jerusalem took 9 of them. What does this mean? The gemara a few lines lower says that the pasuk in Shir Hashirim 8 "achos ketana yesh lanu v'shadayim ain la" refers to Eilam that merited to learn Torah but not to teach torah. So the breasts represent the source of spiritual sustenance, (see also my Rebbie's zt"l hesped for his brother the Rav zt"l - about "birchos shadayim v'racham") and this is the yofi of Yerushalayim: Bava Basra 21a discusses the educational system and how Ben Gamla is to be commended for without him, Torah would have been forgotten in Israel. One of the takanos in teaching was that the children should be brought to Yerushalayim to learn as the pasuk says (Yeshaya 2) "ki mitzion teitzei Torah u'Dvar Hashem Miyrushalayim." Tosfos, s.v. Ki Mitzion says "because they would see great holiness and Kohanim busy in the Avodah, it would direct the heart more to the fear of heaven and to learn Torah, as the Sifrei expounds on the pasuk "l'maan tilmad l'yirah." Great is Maaser Sheni that it brings to [Torah] study, because they would stand in Yerushalayim until he ate his Maaser Sheni and he would see everyone busy in the work of heaven and avodah, he would also be directed toward yiras shamayim and to busy himself with Torah." Also, Rambam Mamrim 1:1 says בית דין הגדול שבירושלים--הם עיקר תורה שבעל פה,
והם עמוד ההוראה, ומהם חוק ומשפט יוצא לכל ישראל. The beis din hagadol in Yerushalayim - they are the main Torah Sheb'al peh, and the pillar of direction (as in teaching or psak), and from them, law and justice emanates to all of Yisrael.
In this context at the seder, shadayim nachonu, the bnei yisrael had the potential to start a great mesoratic tradition but "at eryom v'ervah," we were naked of mitzvos. We had nothing to transmit.
Now, on Pesach night, when we have to see ourselves as being freed from Egypt, a time when the Jews were were commanded several mitzvos, and specifically the seder night with the mitzvah of "vehigadta levincha" which includes teaching the halachos of the seder, not only the story of the exodus (see the answer to the Ben Chacham, and see Hagaddah Siach Hagrid), we have a responsibility and an obligation to teach Torah to our children (and other people).
(The night of the seder is indeed dedicated to the mesorah, as we have a requirement to recite the drashos on the psukim of bikkurim. My rebbe shlit"a mentioned Tshuvos Hagaonim against those who skipped the drashos, they were suspected of being karaim. I think the Rav in Siach Hagrid also discussed the importance of reciting the drashos.)
(Back to my bubbie - I said she transmitted to me Torah attitudes. She taught me how to give tzedaka. She taught me how to respect talmidei chachamim. She told me how to soak and salt meat, to kasher it, etc.)