Why do pet fish eat the rocks at the bottom of the aquarium?

If you mean when they nip at the rocks, then they aren't eating the rocks, they are eating the things on the rocks. It's referred to as grazing by most people I know. There's algae and remaining fish food in/on the gravel- fish take any opportunity to eat, unless they are sick or picky. read more

If you look closely enough, they don't actually ‘eat’ the sand/rocks at the bottom, they simply seem to filter the fine grains. When food pellets are dropped into the aquarium, some of them dissolve in water to form tiny micro pellets that settle at the bottom. read more