This whole page teaches Rabbi Eliezer’s opinions and their derivations in the matter of mitzvahs that override Shabbos, as well as their facilitating actions. The Sages, however, held like Rabbi Akiva who ruled that even if a mitzvah’s performance overrides Shabbos, its facilating actions do not. Why do we spend so much time on the overruled, minority opinion? Because we have enormous respect for the great Rabbi Eliezer and for the process of legal decision-making itself. Rabbi Eliezer had a secular, privileged youth and he gave it all up to pursue Torah. His rulings on the measure of barley brought during Passover, the loaves brought on Shavuos, the four species brought on Sukkos, the sukkah itself, the matzah of Passover and the shofar blasts of Rosh Hashana. Each requires a ruling and none of them can provide a precedent for the others because each carries a crucial particularity. Also, why women are holier than men.