According to simple dualism, our immaterial souls are the bearers of our mental states and we are these souls. We have bodies, but the bodies are not parts of us. We are wholly immaterial.
If the motivation for simple dualism is that only an immaterial soul can have mental states, then we should think something similar about higher animals like dogs and octopuses. Thus, in Rover the dog just as in Alice the human, the soul is the bearer of mental states, and the body is not a part of the soul. Now, the name “Alice” on simple dualism refers to the soul, so that “Alice is in pain” means that she is the bearer of the pain and “Alice has a broken leg” means that the leg associated with Alice is broken (compare: “Alice has a broken bicycle”) rather than that a part of Alice is broken. Surely, “Rover is in pain” and “Rover has a broken leg” mean something very close to “Alice is in pain” and “Alice has a broken leg”, respectively. Thus, “Rover” on simple dualism also refers to the soul.
Furthermore, Rover might be Alice’s pet. And the kind of interspecies affection that might exist between Rover and Alice requires that Rover be the right kind of thing to have affections and other mental states, and so, once again, “Rover” must refer to the soul.
But of course we also say that Rover is a dog. The simple dualist now has two options. The first is to take literally the statement that Rover is a dog, and conclude that dogs—and presumably other higher animals—are immaterial souls (if Rover is immaterial and Rover is a dog, then Rover is an immaterial dog; and Rover surely does not differ radically from other higher animals). Thus, strictly speaking, biologists don’t primarily study dogs and octopuses but rather their bodies, and we have never seen any higher animal.
The second option is to deny that Rover is literally a dog. This presumably requires denying that we are literally homo sapiens. Rather, “Rover is a dog” is to be understood as shorthand for “Rover ensouls a dog.”
Neither option looks attractive. I conclude that Rover is not a soul, and neither is Alice.