I also find "non-human animal" and "human animal" a bit much. It's the language used in the discipline of Animal Studies so I use it. Also, I think there is something to the notion of reminding humans that they are animals, part of the same evolutionary tree as every other animal. As recently as Descartes that wasn't the dominant belief. That said, for those who don't believe in evolution, humans are humans and animals are animals and that's that.