I would agree and say that not only are we not separate from animals, but we are connected with everything earthly as well as otherworldly in a way for which it is difficult to find expressions except in art and poetry. However, and this is peculiar to us human beings, we do not find any other living being, apart from ourselves, that is so conscious of itself and suffers so severely from this consciousness of itself.
No fish that we have ever seen emerge from its habitat and play the harp, no bird that glides through the air ever invent a car, no dolphin climb Mount Everest. It may escape us because we don't speak dolphin, fish or bird and what inventions the animals have devised. We will not know if they have awarded Nobel Prizes among themselves or opened nightclubs. We simply anthropomorphise everything we see and observe, love and hate. Because we are so much human. That which we have in common with the animalistic we want to suppress, you can see it in everything that is suppressed as spontaneous sensations: angry screaming, maniacal crying, unrestrained laughter, nakedness, etc. This schizophrenia, the agony of suffering in the consciousness of oneself, is what distinguishes us from the animal, I think. What torments the soul is understood by every human being, is it not? But what soul actually is, no one can explain. The torment is one thing, because one feels strange, so often alone in this world. And yet there is a great joy, spontaneity, bliss, tending to be in younger still carefree people (though not the rule), that we can laugh at paradoxes immediately, this humour. The schizophrenic is the normal, because every human being can put himself into countless characters, otherwise we wouldn't even know what a character is, couldn't follow a play or a novel. This being torn between the individuality of the self and the group, I don't think animals as we see and observe them in the world have such split personalities.
Yes, in the sense of animated, ensouled, you could take that generic term and it wouldn't be wrong. But definitions are the only thing where we can create contrasts, so we need them and we say to ourselves "we humans" and not "we animals", simply because we are not :)