Have you ever seen the movie Airplane!? If you haven't, go see it, it's the funniest movie of all time.

Anyway, in that movie, the pilot, co-pilot, and flight engineer (from back when commercial planes still had engineers) all become deathly ill from food poisoning from eating the same in-flight meal, and the plane has to be landed by one of the passengers. And although it may all be a big joke in the movie, that is the exact situation that rule is meant to prevent. It's not actually mandated by law (at least not by the FAA) but it is policy for most airlines.