Beitzah 19 - Cooking and eating the sacrifices

On Holiday (Yom Tov), one is allowed to cook. In this, Holidays are different from Shabbat, when cooking is not allowed. Since peace offerings are cooked and eaten, one can bring peace offerings on a Holiday. By contrast, the burnt offering is consumed entirely by fire on the Altar, and no part is eaten. Because it lacks the permission to eat, it should not be brought on Holidays. That is the opinion of Beit Shammai. 

However, Beit Hillel allows bringing even burnt offerings on Holiday. What is their logic? The Torah said, "You will celebrate to God." Whatever sacrifices are needed, you will bring them. It has nothing to do with the permission to cook on Holiday.

This seems like a simple disagreement. It becomes complicated because each view changes to which of the three Holidays it is applicable, before the Holiday or after, and so on.

Art: Young Woman in the Kitchen  by Andres Commodi