Question: Why do Jews eat fish on Shabbat?
Answer: Eating fish on Shabbat is an ancient Jewish custom; it is even mentioned in the text of several Shabbat zemirot (e.g., “Ma Yedidut” and “Yom Zeh M’Chubad”).
Rav Menachem Mendel of Kotzk (Amud HaEmet, p. 72) suggested the following rationale. Most kosher animals have mitzvot performed on them prior to being eaten –shechitah and melichah for example. Fish are the exception. They have no mitzvah or special ritual performed on them. Hence, to make up for this lack, we eat fish on Shabbat – thus associating fish with the tremendous mitzvah of Shabbat.
This reason may also explain why some people are careful to eat fish not just at one of the Shabbat meals, but at all three.