Beitzah 2 - An egg
If an egg was laid on a holiday (Yom Tov), Beit Shammai say that it can be eaten, but Beit Hillel prohibit it. Since one can cook food on a Yom Tov, he won't have to eat the egg raw, but can make a dish.
How are we to understand this argument? If the hen that laid the egg is designated for food, then the egg is part of it and is considered food; how could Beit Hillel prohibit it? And if that hen is kept only for laying eggs, then the egg was not designated for use before the Yom Tov and is therefore "muktzeh", an item that cannot be handled, much less eaten!
Rav Nachman ventured this explanation: Beit Shammai do not accept the whole concept of mukzeh. Moreover, the don't even accept a prohibition of "newly created," or "nolad" - something that was not here at all, and appeared just now, on a Yom Tov. Therefore, there is not reason not to eat the egg. Beit Hillel, on the contrary, subscribe to both prohibitions.
That explanation is very strange though. Usually Beit Shammai is the strict one! How can they be more lenient? Moreover, the explanation is self-contradictory. In other places, in the laws of Shabbat, Beit Hillel are said to follow Rabbi Shimon (no mukzeh), and here, in the laws of Yom Tov, they follow Rabbi Yehudah (yes mukzeh)?
Actually, there is no problem. Who wrote down the rules (Mishna?) - this is Rabbi Yehudah the Prince. In the laws of Shabbat, when cooking is not allowed and people are naturally more careful, he formulated the rules leniently. But in the laws of Yom Tov, where cooking is allowed and people may extend the permissions even further, he formulated the rules more stringently.
Art: Still Life With Bread And Eggs By Paul Cezanne