Just to further clarify what I think is wrong with Margaret Somerville’s “personhood” argument discussed below: she essentially wants to evacuate the notion of person of any substantive content and make it coterminous with human being. Thus, saying that a human animal is a person isn’t a factually informative statement; it becomes a tautology.
Note, though, that once this move is made, the possession of personhood can no longer function as a reason for according special moral status to human beings. “Being a person” and “being a human being” are, on this view, just two different expressions for the same status.
But this is surely not what traditional moral philosophers (e.g., Kant) had in mind when they distinguished between persons and non-persons. For them, persons had special moral worth because of some property that persons–and only persons–possessed such as the ability to follow the moral law. This is why, on the traditional view, it makes sense to ask whether there can be non-human persons, whether terrestrial (e.g., dolphins) or extra-terrestrial (e.g., space aliens or angels). On Somerville’s view, it would literally be nonsensical to ask if there could be non-human persons.
Now, personally, I’m not sure personhood is even a particularly important concept for morality, but that’s a whole other post.