You won’t find the number 13 on an elevator, but we’re beginning פֶּרֶק י״ג in Yevamos and in its introduction ArtScroll notes that a woman cannot accept kiddushin on her own behalf and become married according to the Torah until she is an adult. However, her father can accept kiddushin on his minor daughter’s behalf, which is derived from the פָּסוּק in פַּרְשַׁת כִּי תֵצֵא which states: אֶת־בִּתִּ֗י נָתַ֜תִּי לָאִ֥ישׁ הַזֶּ֛ה לְאִשָּׁ֖ה. If she is divorced or widowed while still being a minor, he cannot marry her off again. So the father’s right is a one shot deal.
ArtScroll adds that in the interest of preventing the exploitation of fatherless girls for promiscuous purposes, the Rabbis instituted that the mother or adult brothers of an orphaned minor girls are empowered to be able to accept kiddushin on her behalf, essentially adopting the role of the father. This is another form of קִידוּשִׁין דְרַבָּנָן. While a minor, a girl at any time can declare her aversion to her husband and leave him without a גֶט through the process of refusal or “מִאוּן” which is essentially a retroactive annulment of the marriage. She can refuse a second marriage (מִאוּן) even while her father is still alive, and she is termed יְתוֹמָה בְּחַיֵי הָאַב because her marital status is the same as an orphan. מִאוּן is essentially a minor’s escape clause.
The Mishnah on דף ק״ז עמוּד א begins with what will basically be five areas of dispute between בֵּית שַׁמַּאי and בֵית הִלֵּל:
#1: בֵּית שַׁמַּאי אוֹמְרִים: אֵין מְמָאֲנִין אֶלָּא אֲרוּסוֹת, וּבֵית הִלֵּל אוֹמְרִים: אֲרוּסוֹת וּנְשׂוּאוֹת
בֵּית שַׁמַּאי is saying that מִאוּן applies only to קִידוּשִׁין (the preliminary stages of marriage) but not נִישׂוּאִין (after the marriage is consummated) but בֵית הִלֵּל says it applies to both.
#2: בֵּית שַׁמַּאי אוֹמְרִים: בַּבַּעַל וְלֹא בַּיָּבָם, וּבֵית הִלֵּל אוֹמְרִים: בַּבַּעַל וּבַיָּבָם
בֵּית שַׁמַּאי is saying that מִאוּן may be directed only at her husband and not at her yavam. In such a situation, she must perform חַלִיצָה in order to dissolve the זִיקָה. But בֵית הִלֵּל says that מִאוּן may be directed at her husband or her yavam.
#3: בֵּית שַׁמַּאי אוֹמְרִים: בְּפָנָיו, וּבֵית הִלֵּל אוֹמְרִים: בְּפָנָיו וְשֶׁלֹּא בְּפָנָיו
A difference of opinion on whether the husband has to be present or not in order for the קְטַנָה to declare מִאוּן.
#4: בֵּית שַׁמַּאי אוֹמְרִים: בְּבֵית דִּין. וּבֵית הִלֵּל אוֹמְרִים: בְּבֵית דִּין וְשֶׁלֹּא בְּבֵית דִּין
A difference of opinion on whether or not the מִאוּן has to be declared in court.
#5: אָמְרוּ לָהֶם בֵּית הִלֵּל לְבֵית שַׁמַּאי: מְמָאֶנֶת וְהִיא קְטַנָּה, אֲפִילּוּ אַרְבַּע וְחָמֵשׁ פְּעָמִים. אָמְרוּ לָהֶם בֵּית שַׁמַּאי: אֵין בְּנוֹת יִשְׂרָאֵל הֶפְקֵר, אֶלָּא מְמָאֶנֶת וּמַמְתֶּנֶת עַד שֶׁתַּגְדִּיל, וּתְמָאֵן, וְתִנָּשֵׂא
בֵּית הִלֵּל said to בֵית שַׁמַּא: She may refuse as long as she is a minor, even four or five times if her relatives married her off again to another man after each refusal. בֵּית שַׁמַּאי said to them: The בְּנוֹת יִשְׂרָאֵל are not to be treated with disregard and should not be passed from one man to another. Rather, she refuses once. And then she must wait until she reaches adulthood and refuse, and marry.
Now to the Gemara, which starts with a discussion of debate #1 above, and cites four reasons why בֵּית שַׁמַּאי says that a fully married קְטַנָה who has done נִישׂוּאִין cannot do מִאוּן:
a) אָמַר רַב יְהוּדָה אָמַר שְׁמוּאֵל: מַאי טַעְמָא דְּבֵית שַׁמַּאי — לְפִי שֶׁאֵין תְּנַאי בְּנִשּׂוּאִין. וְאִי נְשׂוּאָה תְּמָאֵן, אָתֵי לְמֵימַר יֵשׁ תְּנַאי בְּנִשּׂוּאִין. Rav Yehuda said in the name of Shmuel that the reason בֵּית שַׁמַּאי says she can’t do מִאוּן is because there are no conditions (תְּנַאי) with regard to marriage. Although אֵירוּסִין can be conditional, the condition is nullified upon נִישׂוּאִין. Likewise, marriage cannot be conditional, as the sexual relationship is not subject to a תְּנַאי. And if a married minor girl could do מִאוּן, others may mistakenly think this to be a condition with regard to the marriage of an adult woman, and they will come to say that there can be a תְּנַאי with regard to marriage. The outcome after several back and forth volleys is that בֵּית הִלֵּל is not concerned that a תְּנַאי. remains in place after נִישׂוּאִין, as they know that the marriage of a minor is only recognized מִדְרַבָּנָן.
b) רַבָּה וְרַב יוֹסֵף דְּאָמְרִי תַּרְוַיְיהוּ: טַעְמָא דְּבֵית שַׁמַּאי, לְפִי שֶׁאֵין אָדָם עוֹשֶׂה בְּעִילָתוֹ בְּעִילַת זְנוּת. Rabba and Rav Yosef both say: Beis Shammai’s reason is that a man would not readily render his sexual act as promiscuous sexual intercourse. If he had intercourse with the minor girl and the marriage was later retroactively annulled by her מִאוּן, then his sexual act was outside the context of marriage and is regarded as זְנוּת. After some volleying, Beis Hillel indicates that they do not regard בִּיאָה under such circumstances as זְנוּת, so there is no stigma attached to having stood under the חוּפָּה with a girl who later does מִאוּן.
c) רַב פָּפָּא אָמַר: טַעְמָא דְּבֵית שַׁמַּאי מִשּׁוּם פֵּירֵי, טַעְמָא דְּבֵית הִלֵּל מִשּׁוּם פֵּירֵי. טַעְמָא דְּבֵית שַׁמַּאי מִשּׁוּם פֵּירֵי — דְּאִי אָמְרַתְּ נְשׂוּאָה תְּמָאֵן, שָׁמֵיט וְאָכֵיל לְהוּ מִינַּהּ, דְּסוֹף סוֹף לְמִיפַּק קָיְימָא. וּבֵית הִלֵּל: אַדְּרַבָּה, כֵּיוָן דְּאָמְרַתְּ תְּמָאֵן — אַשְׁבּוֹחֵי מַשְׁבַּח לְהוּ. סָבַר דְּאִי לָא, עָיְיצִי לַהּ קְרוֹבֵיהּ, וּמַפְּקִי לַהּ מִינֵּיהּ. The outcome here is that Beis Hillel says the husband thinks to himself: “Since she may do מִאוּן, he will seek to improve her property. He will think: if I do not do so, her relatives will advise her to do מִאוּן and they will take her from me.
d) רָבָא אָמַר: הַיְינוּ טַעְמָא דְּבֵית שַׁמַּאי — שֶׁאֵין אָדָם טוֹרֵחַ בִּסְעוּדָה וּמַפְסִידָהּ. וּבֵית הִלֵּל: תַּרְוַיְיהוּ נִיחָא לְהוּ, כְּדֵי דְּלִיפּוֹק עֲלַיְיהוּ קָלָא דְאִישׁוּת. Rashi points out that in Talmudic times, the goom’s family would prepare a wedding feast which would take place at the time of the נִישׂוּאִין. Beis Shammai holds that if מִאוּן was in play at the time of the נִישׂוּאִין, the husband would not not risk investing in the feast at the risk of the marriage being called off. But Beis Hillel says we’re not worried about. As long as they’re happy. set up the carving stations and enjoy!
The Gemara then goes on to discuss debate issue #2 above, proceeding through #5. For coverage on that in detail, I leave you with Rabbi Stern’s video: