I have been studying Vitamins for a while (Nutritional Biochemistry), and though I agree with the explanation of your teacher and with the answers already given,
Part of the reason has to do with their discovery:
The general definition of vitamins is described:
The vitamins are a disparate group of compounds; they have little in
common either chemically or in their metabolic functions.
Nutritionally, they form a cohesive groupof organic compounds that are
required in the diet in small amounts (micrograms or milligrams per
day) for the maintenance of normal health and metabolic integrity.
They are thus differentiated from the essential minerals and trace
elements (which are inorganic) and from essential amino and fatty
acids, which are required in larger amounts.
In addition to systematic chemical nomenclature, the vitamins have an apparently illogical system of accepted trivial names arising from the history of
their discovery.
For several vitamins, a number of chemically related compounds show the same biological activity, because they are either
converted to the same final active metabolite or have sufficient structural similarity
to have the same activity.
I believe initial classification was based on two forms- fat solubility and water solubility. It must have been elucidated through experiments with milk:
When it was realized that milk contained more than one accessory food
factor, they were named A (which was lipid-soluble and found in the
cream) and B (which was water-soluble and found in the whey). This
division into fat- and water-soluble vitamins is still used, although
there is little chemical or nutritional reason for this, apart from
some similarities in dietary sources of fat-soluble or water-soluble
vitamins
Indeed the "Vitamin B Family" has a lot of compounds (riboflavin, pantonthenic acid, biotin, thiamin, niacin, cobalamin etc) that are structurally unrelated,
but were grouped possibly due to their discovery as they either had similar chemical property-water solubility abeit some forms of vitamins (e.g ascobic acid) are water soluble.
This division into fat- and water-soluble vitamins is still used,
although there is little chemical or nutritional reason for this,
apart from some similarities in dietary sources of fat-soluble or
water-soluble vitamins. Water-soluble derivatives of vitamins A and K
and fat-soluble derivatives of several of the B vitamins and vitamin C
have been developed for therapeutic use and as food additives
As the discovery of the vitamins progressed, it was realized that “Factor B”
consisted of a number of chemically and physiologically distinct compounds.
Before they were identified chemically, they were given a logical series of alphanumeric
names: B1, B2, and so forth
From a pharmaceutical perspective...
The "complexity" of vitamin B compounds simply suggest a combination of different compounds that fall under this family. Because vitamin
compounds are required in relatively large amounts compared to fat soluble counterparts, it makes sense to combine them as supplements rather than packaging
7+ pharmaceutical products as "Vitamin B1", "Vitamin B2", "Vitamin B3"... suplements, it creates more confusion and non-compliance instead their systematic names are used for example pyridoxine injection (vitamin B6), Nicotinamide tablets but where multivitamin are prescibed its just a "complex" of there compounds usually 5-6 of these "B" vitamins.
It is important to note that such compounds are requirement in very small quantities/day, and overdosing (through such these compounds can cause undesirable side effects).
Other forms of vitamins (fat soluble) are equally important but most of them are either stored in body in reserves e.g Vitamin A, others like Vitamin K are synthesised in the body by bacteria hence are needed in very small amounts
This is the chief reason why there are fewer supplements of such vitamins (although they may be needed in special cases).
For a compound to be considered a vitamin, it must be shown to be a
dietary essential. Its elimination from the diet must result in a
more-or-less clearly defined deficiency disease, and restoration must
cure or prevent that deficiency disease.
Several forms of vitamin D?
Vitamin D is not strictly a vitamin, rather it is the precursor of one
of the hormones involved in the maintenance of calcium homeostasis and
the regulation of cell proliferation and differentiation, where it has
both endocrine and paracrine actions.
The name vitamin D1 was originally given to the crude product of irradiation of ergosterol,
which contained a mixture of ergocalciferol with inactive lumisterol (an isomer of ergosterol) and suprasterols. When ergocalciferol was identified
as the active compound, it was called vitamin D2. Later, when cholecalciferol was identified as the compound formed in the skin and found in foods, it was
called vitaminD3.
Remarks
The "Vitamin B" naming of these compounds must have been through discovery, and no clear experiments had accurately produced identity of these compounds, there were named as they were discovered but since they have been identified they they now have systematic names
abeit vitamin B still being used today and are formulated as "vitamin B complexes" in pharmaceutical products (perhaps to avoid confusion) hence systematic names are used (folic acid, pantonthenic acid, biotin, thiamin, niacin, cobalamin etc) I have never come across complexes of other Vitamins. Remember for a compound to be named a vitamin it must fit the description above, but I am not disputing the fact that other compounds with similar biological activities exist as "K" group.
References
- Nutritional Biochemistry of Vitamins (Bender)
- Nutritional biochemistry (Brody)
- Modern Nutrition in Health and Disease (Rosset al)