I guess the downvote is because you are not really adding anything to the discussion because it is obvious what they meant.
Some of those vestiges can be found in our language. Here, it was saying "human and animals" instead of the more correct "human and other animals" (without the emphasis of course). This kind of phrasing tend to promote the higher status of humankind as self evident, while frankly it is not. (I've read once that Dolphins may be almost as sentient and sapient as we are. In this case, they should have right they currently don't have.)
We now know that making up a category that includes all fishes, insects, birds, reptiles… and all mammals (including apes), but Homo Sapiens and some of its now extinct cousins isn't reasonable.
Unless of course if you believe that humans have immaterial souls and animals do not. That would make us very special. But the probability I assign to this possibility is negligible.
By "wrong" I essentially meant "you shouldn't do that", here because it is misleading. Using the single word "animal" when you actually mean "non-human animal" suggest we humans are not animals. We are.
Now you changed my mind a bit: the "non-human animals" category does have its uses, and it does make sense to think of it. I just think it doesn't deserve the shorter expression "animals".
Like which ones? The useless (to dolphins) ones such as freedom of speech or owning property, or the ones many humans don't have like kind treatment and living in an uncontested land like they used to?
I suspect however that once the world treats its humans well (if ever), then the other animals will also be in much better shape.