Biology is the study of life; microbiology the study of microscopic life. While the virus is certainly microscopic, to consider why viruses should be included under microbiology is to examine what makes the virus a life form and not simply a replicator.
There is no universal agreement on precisely what constitutes the quality of life. However, common elements frequently include adaptive reproduction, metabolism, growth, homeostasis, and the ability to respond to a stimulus. Of these, the first is perhaps the point of greatest consensus.
All life has the ability to reproduce itself directly or through kin selection, especially inexact copies of itself which may be better adapted to an altered environment than the parent organism. Viruses are capable of such reproduction, but only with the assistance of a host cell. While some accept only species-independent reproduction as fulfilling the requirement to be alive, symbiotic reproductive arrangements do exist even in the macroscopic plant and animal world: including our familiar domestic wheat, which is no longer capable of reproduction without human assistance.
Living things are able to metabolise non-living materials into their own component structures, and additionally into the energy needed to grow and maintain those structures. Again, viruses are capable of doing this only with the assistance of a host cell. In this age of probiotics, it has become a matter of popular knowledge that humans too are dependent on their colonies of internal symbiotic bacteria, without which we would be unable to metabolise much of what we consume.
All life responds at the very least to those stimuli which could represent a source of energy (food). Viral structure alters in the presence of appropriate host cells so as to be able to enter them and fit itself into their metabolic and reproductive structures. Viruses can also respond to long-term negative (but not killing) stimuli by shifting into an inert crystallene structure; which nevertheless remains capable of shifting back into active virulent form in the presence of an appropriate host cell stimulus. This crystallene structure is how a few laboratories still store the smallpox virus.
Finally, living things are capable of regulating their internal environment through positive and negative feedback cycles to maintain a constant condition. While viruses are capable of altering their internal environment, the question of true homeostatic regulation is much less certain. Some viruses do achieve reproductive homeostasis, where the viral reproductive material continues to exist within the host cell mostly in a dormant state, and is replicated by the cell each time the cell replicates itself.
By most of the criteria by which life is identified, viruses do seem to be alive; and thus should be included under microbiology rather than organic chemistry.