So what does he want to be called? Just a rat? But - there are actual rats, which are already called rats. Unless those don't exist in this universe, "ratman" seems like a pretty reasonable term. He has both rat and humanoid features.
Yeah. Him calling the man "man-rat" makes no sense though. For it to make sense, there would have to be something even more human and more distant from rats, so that he could be viewed as half rat.
It's a false equivalency on the Ratman's part. There exist rats. There exist men. He's a cross somewhere between, where the man is just a man. I mean, provided there isn't some kind of miniature, unintelligent human analog in this world.