I just had a really naive thought. Let's imagine what a definition of animals would be like. It would say something like this: Animals are things that maintain homeostasis, take in nutrients and grow, reproduce, initiate and control a large variety of types of motion in response to changing environmental features, etc. It's not very easy to come up with details of the definition, but it seems like it would go something like this. Well, it's pretty clear that we do these things, as well as doing any plausible items we'd want to add to the definition. So we're animals. Case closed.
What could an anti-animalist say? I guess her best hope would be: The definition is close to the truth, but not quite. Rather, animals are things that non-derivatively maintain homeostasis, take in nutrients and grow, etc., etc. But it seems to me that there is a natural dilemma. Derivative homeostasis (say) either is or is not a case of homeostasis. If it is, that seems all we need for animalhood (along with analogous other qualities). If it is not, then the anti-animalist can't say that we have homeostasis, and that's absurd.