I think the other posters are correct that animist beliefs aren’t being correctly summed up.
Still, to address it in Thomist terms, we expect the properties of a thing with a specific essence (definition) to be what reveals the essence to us. I’m not aware of any rock or tree which demonstrates any properties that should follow from sentience or rationality.
I’ll add that we’re of course familiar with human persons who fall into a vegetative state. Still, from a broad survey of human persons, one can know that such cases are aberrations, cases where something has gone wrong and the properties we know are standard are failing to manifest themselves because of how things went wrong. But no rock has nutritional, sensitive, or rational powers we’d associate with living the things. And while a tree has properties that point to nutritional/vegetative powers, no tree has properties that point to a sensitive or rational essence. And while dogs demonstrate powers we’d associate with a sensitive essence, they don’t demonstrate any we’d associate with a rational essence. If we don’t see properties that point to these things, it seems we’ve no reason to suppose they have these things.
But I’ll leave it to the animist to (1) define their actual beliefs and (2) provide an argument as to why we should believe the positive claims.