Yevamot 107 - Underage wife
People used to live short lives, and their next day was uncertain, so early engagement and marriage were important. The Torah provides legal authority for the father of a girl to give her away in marriage before she reaches maturity. However, if the father was not alive, getting married was a problem: the underage girl lacked legal authority to accept an engagement for herself, and in her family the Torah gave this authority only to her father. Therefore, the Sages instituted for the mother and the girl's brothers to arrange her marriage. Yet, since the legal basis for this marriage lied in the authority of the Sages, and not in the Torah, it could be dissolved by the girl deciding that she does not like her husband and does not want to continue the marriage. This is called a "miyun," or "refusal." How exactly does this happen?
Beit Shammai say that she can refuse the marriage only after engagement but not after the marriage is complete with the chuppah. Had refusal been allowed when they are already living together, people might make a mistake and say that in general marriage with an adult woman can be dissolved without a divorce (Get), perhaps if the marriage conditions were not fulfilled. However, Beit Hillel allow her to refuse anytime: people know that a marriage of a minor girl is special and can be dissolved without a Get.
Another type of logic: Beit Shammai say that if the girl can walk away, the man will not prepare the weddings reception, with all associated expenses, just to see it go to waste. However, Beit Hillel allow her to refuse any time: both the man and the woman want their wedding to be known, so the man will not hesitate to throw a feast in order to get married.
Art: Wedding Dinner by Jacob Gerritsz by Van Hasselt