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I've never heard the "odd number" thing. Commonly, pet stores will tell you that certain fish need to be kept in groups, the number they give is usually 5, but sometimes 3.
Having small groups of fish is done for two reasons - to build the schooling behavior (usually 5 or more fish) or to deflect aggression (3 or more). Still, that doesn't always help - green chromis for example will school in the wild, but in aquariums, they often pick on the smaller, weaker members of their group. Anthias schools often change dynamics as fish turn into males and fight more.
Then, there are actually two different terms; schooling and shoaling. Schooling fish form strong bonds and use that to travel in safety. Shoals are looser assemblages of fish that just sort of "hang out" together. They can even be different species. Most marine aquarium fish form shoals.