I guess it depends on how happy you want the fish. You can keep a fish alive in a tiny space but it won't be happy.
For example, would you like living your entire life in a closet where you ate, slept and pooped all in that closet for years? Wouldn't it be easier if instead of that closet you got an appartment or an entire house? There would be a lot more room. Its the same with fish usually. The more room there is the better off they usually are.