Avoiding a course in fish biology, I will try to explain this as briefly as I can.
A species of freshwater fish that lives in groups of its own species can be termed shoaling or schooling. Regardless of which term may be the correct one, the principle behind it is the same. This trait is imbedded into the species' DNA. All sorts of other inherent traits and behaviours and needs are also programmed into the species' DNA. So as the fish grows, it "expects" specific things to be part of its life. When one or more of these traits is missing, it affects the fish's well-being. As the citation [in green in my signature] from Paul Loiselle says, "It is inhumane to deprive any animal of an element it regards as critical to its well-being, and totally naive to expect normal behavior in its absence." Aside from direct interference to the functioning of the fish's metabolism (depending upon the factor missing), this causes stress.
Stress is the root cause of almost all disease and health problems of aquarium fish. Today we recognize that the health of any living organism is directly related to the level of stress inflicted upon it; for fish this is a major problem because the fish cannot do anything to reduce or eliminate it—they can only fight it or succumb to it. Our fish are confined to the small space of their aquarium, and only the aquarist can control their environment. In a very real sense, we are directly responsible for any and all stress inflicted upon the fish. We must understand what stress is and how it harms our fish. Here is how Biology Online defines stress:
The sum of the biological reactions to any adverse stimulus—physical, mental or emotional, internal or external—that tends to disturb the organisms homeostasis; should these compensating reactions be inadequate or inappropriate, they may lead to disorders.
Homeostasis is defined as “the tendency of an organism or a cell to regulate its internal conditions, usually by a system of feedback controls, so as to stabilize health and functioning, regardless of the outside changing conditions.” Physiological homeostasis, or physical equilibrium, is the internal process animals use to maintain their health and life: “the complex chain of internal chemical reactions that keep the pH of its blood steady, its tissues fed, and the immune system functioning” (Muha, 2006). Stress makes it more difficult for the fish to regulate the normal day-to-day physiological functions—the homeostasis—that are essential to its life.
So, in a nutshell, denying the fish a group of its own is creating an adverse situation that the fish cannot escape from, and which will slowly debilitate its health.