af hein ha'yu b'oso hanes -- kiddush, matzah, 4 kosos, etc.

There is a teshuvah from the Mahara”m m’Rotenberg (I’m not such a baki – R’ Ovayda z”l quotes it in Yechaveh Da’at 2:65) that asks why we need the hekesh of zachor to shamor to obligate women in the mitzvah of kiddush – why not say they are obligated because of af hein ha’yu b’oso ha’nes?  We say in kiddush that Shabbos is zecher l’yetzi’as Mitzrayim and women also experienced the nes of being taken out of Egypt.  The Mahara”m m’Rotenberg answers that “oso hanes lo shayach l’kiddush.” 

Before getting to what he means by the answer, it’s clear from the question that the Maharam m’Rotenberg held that the sevara of af hein can create a chiyuv d’oraysa.  By way of contrast, Tosfos (Meg 4b) explains that we need to learn that women are obligated in the mitzvah of matzah from a hekesh to chometz because af hein can create only a chiyuv derabbanan, not d’oraysa.  Tosfos gives another answer as well (see also Tos Pesachim 108), perhaps because other ba'aleu Tos. disagreed and held like this Maharm m'Rotenberg.  

It sounds like what the Maharam m’Rotenberg means by his answer is that although there is a chiyuv to mention yetzi’as Mitzrayim in kiddush, yetzi’as Mitzrayim is not the mechayeiv of kiddush – Shabbos is the mechayeiv.

Rav Soloveitchik independently developed the same idea in a letter to his father (quoted in the Igros haGRI”D, Hil Chanukah).  Why is it that if one has only enough funds for either kiddush or ner Chanukah, ner Chanukah takes precedence because of pirsumei nisa [see Shu”T Avnei Nezer #501] –- is there not also an element of pirsumei nisa in reciting kiddush and mentioning yztei’as Mitzrayim?  RYBS answered that although kiddush may incorporate a kiyum of pirsumei nisa in that yetzi’as Mitzrayim is mentioned, pirsumei nisa it is not the mechayeiv of the mitzvah.  Only the mitzvos of 4 kosos, ner Chanukah, and mikra megillah share that quality.

This sevara answers Tos question as to why we cannot use af hein to create a chiyuv of achilas matzah.  Achilas matzah may incorporate a kiyum of pirsumei nisa in that it reminds us of the nes of yetzi'as Mitzrayim, but the mechayeiv of the mitzvah is not pirsumei nisa.