As we learned in the first Mishna (see above, daf 2), Shammai and Hillel disagree about when a woman who menstruates is considered a nidda with regard to making things that she touches ritually unclean. Shammai rules that she only makes things unclean from the time she sees menstrual blood; Hillel rules that everything with which she came into contact since the last time that she examined herself for purity will be rendered unclean.
The Mishna offered a third opinion – that of the Sages – which disagrees with Shammai as being too lenient and with Hillel as being too strict. According to the Sages, only those objects that the woman touched during the previous 24 hours will be rendered unclean, unless she had examined herself during that period, in which case only those objects that the woman touched since that examination will be rendered unclean.
The Gemara on today’s daf discusses the basis for the Sages’ ruling. Rabbah suggests that the stringency of Hillel is unnecessary because a woman who begins to menstruate feels a sensation in her body. Abayye objects to this explanation, arguing that in that case the woman should become ritually unclean only at that moment, as Shammai taught! The Gemara explains that Rabbah was aware of this and that he made this suggestion only to test and sharpen (le-hadudei) his student, Abayye.
This educational method – where an explanation is suggested that cannot be correct – is found a number of times in the Talmud. There are even cases where the teacher acts in a manner that contradicts his teaching and the Gemara explains that he did so in order to sharpen his students. Rashi explains that the purpose of such a test was to encourage the students to come up with their own explanations, or, as the Ritva explains, for the purpose of review so that students will recall what they learned in a spontaneous manner.