Rabbi Chanan said: what is the verse [for being unworthy of kindnesses]? "I have become small from all the kindnesses" (Genesis 32:11). Rabbi Zeira on a windy day would not go out among the palm trees [lest one fall]. Rav Yitzchak bar Rav Yehudah said: a person should always pray that he not fall ill, for if he falls ill they say to him: bring merit and be acquitted, as it is said, "for the one who falls may fall from it" (Deuteronomy 22:8), "from it" [meaning] he must bring proof [of his merit to be saved]. Why were these [three commandments] entrusted to the woman? She extinguished the lamp of the world, as it is written, "the lamp of the LORD is the soul of man" (Proverbs 20:27); therefore let her keep the commandment of the lamp. She defiled the dough-offering of the world, this is Adam the first man, as it is written, "and a mist went up from the earth" (Genesis 2:6), and adjacent to it, "and the LORD God formed the man" (Genesis 2:7), like a woman who kneads her dough with water and afterward takes the dough-offering; therefore let her keep the commandment of challah. She spilled the blood of Adam the first man, as it is written, "whoever sheds the blood of man, by man shall his blood be shed" (Genesis 9:6); let her keep her menstrual laws, that it may be atoned for her. Rabbi Yehoshua ben Levi said: a man is obligated to visit his wife at the hour he goes out on a journey, as it is said, "and you shall know that your tent is at peace, and you shall visit your dwelling and not sin" (Job 5:24). Is this derived from there? It is derived from here: "and to your husband shall be your desire" (Genesis 3:16), teaching that the woman longs for her husband at the hour he goes out on the road. This was needed only for [the time] close to her menstrual period; and although the Rabbis said a man must separate from his wife close to her period, this applies to a voluntary act, but for the sake of a commandment it does not apply.
Why the Three Commandments Were Entrusted to Women
Yalkut Shimoni on Torah 32:1
אָמַר רַבִּי חָנָן, מַאי קְרָאָהּ (בראשית לב, יא) "קָטֹנְתִּי מִכָּל הַחֲסָדִים" רַבִּי זֵירָא בְּיוֹמָא דְשׁוּתָא לָא נָפִיק בֵּינֵי דִיקְלֵי אָמַר רַב יִצְחָק בַּר רַב יְהוּדָה, לְעוֹלָם יְבַקֵּשׁ אָדָם רַחֲמִים שֶׁלֹּא יְהֵא חוֹלֶה, שֶׁאִם חָלָה אוֹמְרִים לוֹ הָבֵא זְכוּת וְהִפָּטֵר שֶׁנֶּאֱמַר (דברים כב, ח) "כִּי יִפֹּל הַנֹּפֵל מִמֶּנּוּ", מִמֶּנּוּ לְהָבִיא רְאָיָה. לָמָּה נִמְסְרוּ לָאִשָּׁה, הִיא כִּבְּתָה נֵרוֹ שֶׁל עוֹלָם, דִּכְתִיב "נֵר ה' נִשְׁמַת אָדָם", לְפִיכָךְ תִּשְׁמוֹר מִצְוַת נֵר, הִיא טִמְּאָה חַלָּתוֹ שֶׁל עוֹלָם, זֶה אָדָם הָרִאשׁוֹן, דִּכְתִיב (בראשית ב, ו) "וְאֵד יַעֲלֶה מִן הָאָרֶץ", וְסָמִיךְ לֵיהּ "וַיִּיצֶר ה' אֱלֹהִים אֶת הָאָדָם", כְּאִשָּׁה שֶׁמְּקַשְׁקֶשֶׁת עִסָּתָהּ בַּמַּיִם וְאַחַר כַּךְ נוֹטֶלֶת חַלָּה, לְפִיכָךְ תִּשְׁמוֹר מִצְוַת חַלָּה, הִיא שָׁפְכָה דָּמוֹ שֶׁל אָדָם הָרִאשׁוֹן, דִּכְתִיב (בראשית ט, ו) "שֹׁפֵךְ דַּם הָאָדָם בָּאָדָם דָּמוֹ יִשָּׁפֵךְ", תִּשְׁמוֹר נִדָּתָהּ שֶׁיִּתְכַּפֵּר לָהּ. אָמַר רַבִּי יְהוֹשֻׁעַ בֶּן לֵוִי, חַיָּב אָדָם לִפְקֹד אֶת אִשְׁתּוֹ בְּשָׁעָה שֶׁהוּא יוֹצֵא לַדֶּרֶךְ שֶׁנֶּאֱמַר (איוב ה, כד) "וְיָדַעְתָּ כִּי שָׁלוֹם אָהֳלֶךָ וּפָקַדְתָּ נָוְךָ וְלֹא תֶחֱטָא". הָא מֵהָתָם נָפְקָא, מֵהָכָא נָפְקָא, וְאֶל אִישֵׁךְ תְּשׁוּקָתֵךְ מְלַמֵּד שֶׁהָאִשָּׁה מִשְׁתּוֹקֶקֶת עַל בַּעְלָהּ בְּשָׁעָה שֶׁיּוֹצֵא לַדֶּרֶךְ. לֹא נִצְרָכָה סָמוּךְ לְוֶסְתָּהּ, וְאַף עַל גַּב דְּאָמוּר רַבָּנָן חַיָּב אָדָם לִפְרֹשׁ מֵאִשְׁתּוֹ סָמוּךְ לְוֶסְתָּה הַנֵי מִילֵי לִדְבַר הָרְשׁוּת, אֲבָל לִדְבַר מִצְוָה לֹא.