Animal definition: any of a kingdom (Animalia) of living things including many-celled organisms and often many of the single-celled ones (as protozoans) that typically differ from plants in having cells without cellulose walls, in lacking chlorophyll and the capacity for photosynthesis, in requiring more complex food materials (as proteins), in being organized to a greater degree of complexity, and in having the capacity for spontaneous movement and rapid motor responses to stimulation.
According to me, to be a vegetarian is rather than a living attitude than a scientific way. You are a vegetarian if you does not eat meat and meat products from breeding animals. Protozoans are not slaughtered and they don't eat corn or wheat, as competitors from vegetal sources for human nutrition. Good luck. JB