Why is the Vitamin B complex, a "complex"?
It is essentially exactly what your teacher says: the term vitamin B complex is used because the structures assigned a name ‘vitamin Bx’ don’t really have anything in common although they are all somewhat important.

As to why nobody ever uses vitamin K complex or vitamin D complex: well, at least in my country those vitamins are very under-represented when compared to ABCE. ABCE vitamins are those often seen as the most important, the most valuable or similar.[citation needed] They are often advertised as being included in supermarket products. The advertising industry probably doesn’t want to ‘establish’ yet another thing they could add but would be rather cost-intensive.