According to the Mishna on our daf, if a yevama comes to court within 30 days after the yibum (levirate marriage) is to have taken place, claiming that the yavam never consummated the yibum, the beit din will obligate him to perform halitza (ceremony releasing one from the obligation of yibum) with her. If the claim is made after 30 days then we request of him that he perform halitza, but we do not obligate him to do so. The Gemara explains that the case of the Mishna is when he contradicts her claim, arguing that he had fulfilled the mitzva of yibum and has now divorced her, so there is no need for halitza. When such a claim is made within 30 days we accept her version, but if they had been living together for more than 30 days we assume that they had certainly engaged in relations, and we accept his version.
One question raised by the rishonim is why we do not force him to participate in the halitza ceremony even in the case where her claim was made after 30 days? Since he has chosen to divorce her, he does not lose anything by performing halitza – so why should he object? In such a case we would anticipate that the principle kofin al midat Sedom should be applied. (The rule kofin al midat Sedom teaches that in an interaction between two people where one person benefits and the other suffers no loss, we obligate the one who will not lose out to accommodate the needs of the person who stands to benefit.)
Tosafot answer that that the yavam can claim that a court appearance is a burden for him, or even that the halitza ceremony is degrading towards him, so he is perceived as suffering a loss should he participate in it. According to the Nimmukei Yosef he can also argue that if he simply divorces her, he reserves for himself the right to potentially remarry her at some point in the future. Performing halitza, on the other hand, would reinstate her status as his brother’s wife and the option to remarry her in the future will be closed to him.