Actually, the rule is that all fish for consumption must have fins and scales that are detachable from the skin. Shellfish does not qualify, nor do lobsters, crabs and other crustaceans.

From a dietary standpoint, the prohibition against eating shellfish is a wise one in sanitarily handicapped environment and pre-refridgeration society. Even with our modern conveniences, lots of people have severe and sometimes fatal allergic reactions to shellfish.