Stewart-Williams has a somewhat muddled argument (hat-tip) that evolutionary theory undermines the foundations on which a thesis of human dignity rests. One of the things that makes his argument muddled is that he fails to distinguish three completely distinct kinds of theses (there are slight variations of each of the following, but the variations are not important here because Stewart-Williams is mixing together entire families):
I. Human Dignity: Human beings ought to have a role in moral reasoning such that they are treated as transcending in value and importance any price and, as such, should be treated with respect and responsibility.
II. Human Uniqueness: No other animals have the sort of feature in light of which people attribute this dignity to human beings.
III. Human Supremacy: All other animals have their value wholly in being instrumental to human ends.
These are all three completely different ideas; although they are consistent with each other, none of the three actually entails any of the others. You can hold that human beings have transcendent dignity without committing to the claim that they are the only ones that do, or that other animals have no value in themselves. You can hold that some feature usually used as a ground for this dignity, e.g., rationality, is unique to human beings without holding that it actually gives the dignity people think it does; and you can hold that it is unique but that there are many other features, available to many other animals, that are valuable in themselves. And you can hold that other animals have value wholly in being instrumental to human ends without holding that human beings are beyond price or that they have unique features. Failing to recognize this comes well nigh to making Stewart-Williams's argument incoherent; he argues against I at one point by arguing against III, and argues against III at one by arguing against II. That is, almost his entire argument consists of rejecting claims by giving arguments against claims that are not the claim he is arguing against at a given moment.
Moreover, even if we take a position which holds I, II, and III, Stewart-Williams misses the mark somewhat. His rejection of II makes the false assumption that the only features that are used to ground human dignity are the image of God thesis -- that human beings are in the image of God -- and the rationality thesis -- that human beings are animals; to give just one example of another feature that has been given as such a ground, some have suggested creative will. His rejection of the image of God thesis is less than adequate; it makes the assumption (again, false) that the only reason for accepting such a thesis is the belief that God created human beings in accordance with a pre-existing design; but this is to confuse questions of how we come to be in the image of God with questions of what it is that makes us like God, and therefore of divine worth, regardless of how we came to have it. His rejection of the rationality thesis is equally weak. He assumes that the primary sense of rationality in this context is "the ability to work things out about the world"; this is vague enough that perhaps it includes everything, but the primary sense in which rationality is relevant to this question is usually understood to be our capacity to engage in abstract moral reasoning -- to reason out moral principles, communicate them, and act according to them. Unlike more technical cognition about tools and coordination, this is not obviously distributed in different degrees throughout the animal kingdom. But even if it were, all this would do is cause problems for II, not I. To hold that all animals should be regarded as having dignity like human dignity in the degree that they are regarded as having rationality is a coherent position.
His rejection of the claim that even if rationality were unique to humans it still would not be a supreme adaptation seems to me to be more muddled still. It is simply wrong to say that after Darwin biology has anything to say at all about what constitutes a "supreme adaptation" or not; it lacks the tools entirely for doing it, since it only deals with the degree of reproductive and survival success. But it's difficult to find cases where people justify the supremacy of rationality in terms of its superior contribution to our survival or reproductive fitness; we usually evaluate rationality as important because it is valuable for moral ends. So the fact that, in biological terms, rationality is just one adaptation among many -- if it really is even quite right to consider it an adaptation at all rather than, from a biological point of view, something of an accident -- is irrelevant to the question. Multiply adaptations as you please; it still remains a question of how valuable any of them are for human valuing, which is, after all, what we are talking about when we are talking about human dignity.
And this is all in the course of one short passage of a few paragraphs; I have to say I don't think it bodes well for the book from which it is excerpted.