Do Fish Eat Their Eggs

Not all aquarium fish will eat their own eggs.  Many of the fish that I've bred at home, like angelfish and Loricariids, will guard their eggs before they hatch.  These types of fish will use their fins to circulate water around the eggs (probably to prevent the eggs from growing fungus) and block or fight off other fish that try to eat the eggs.  (Mouth-brooders are an even more extreme example, as are discus, which allow their fry to feed off slime they secrete from their bodies.)  We usually remove these eggs from the tank not to protect them from their parents, but to protect them from other fish.

As Anthony said, it's definitely energetically more favorable to a fish to eat its own eggs, if it thinks the eggs are going to get eaten by other fish or won't hatch.  However, aquariums are very different from the wild, so many aquariums may have conditions that fish parents might view as "unfavorable" - that's one possibility for why fish do this.