Beitzah 18 - Purifying water
Before the Holiday (Yom Tov) one must try to purify himself, by immersing in a mikveh - because of the multiple sacrifices that will be brought on a Yom Tov. This includes the person, utensils, and even (we will define the circumstances) water. However, if the Yom Tov follows right after Shabbat, then everything must be purified before Shabbat - so say Beit Shammai. Beit Hillel basically agree, only they make an exception for the person himself and allow him to go to the mikveh even on Shabbat.
Why can't we purify utensils - they are very much needed! - Because one may come to carry them on Shabbat. Good, but if so, purifying them in one's own courtyard should be permitted! - No, that is an additional precaution, lest one comes to carry in the street. But do we ever make such additional decrees? Talmud tries to prove that we don't, but confutes all such proofs. Another explanation: it is prohibited to purify utensils as a precaution against wringing them. What about non-cloth? - Again, additional decree protecting the first one. Again, we go through the proofs that such decrees exist.
There is also a third explanation - that one may delay immersions. Now that he knows that he cannot do it on Shabbat, he will rush. The fourth: it appears as if he fixes things on Shabbat. But if so, we should forbid personal immersions!? - No, he looks as if he is cooling off. Again, we go through marginal cases like cooling off in dirty water, and find justifications for these too.
Art: Peasants drawing Water from a Fountain by Gioacchino Assereto