Why is a virus not considered a living organism?

Because it lacks the metabolic components needed for reproduction and proliferation. As you may know it's a parasite living by exploiting other living Organisms.

Virus are the organisms that contains DNA or RNA as their genetic material. The virus has the ability to infect the bacteria and the other forms of the living organism.

Virus are considered non-living because outside the host organisms, they do not perform any cellular activities or the activities perform by the living organisms. Once, they enter in the host they start grow and multiply their numbers.