Is the argument from marginal cases obtuse?

Elizabeth Anderson claims that the argument from marginal cases is 'the central argument' behind the claim that nonhuman animals have rights. But she thinks, along with Cora Diamond, that the argument is 'obtuse'. Two different meanings could be intended here: that the argument from marginal cases is too blunt or dull to dissect the reasons why it makes sense to say that nonhuman animals have rights or that the argument from marginal cases is insensitive regarding nonrational human beings (the marginal cases of humanity). The purpose of the present article is to argue that, despite Anderson's and Diamond's nuanced and perceptive treatments of the argument from marginal cases, this argument is not obtuse in either sense of the term.