One of Cohen's arguments is to attack an analogy of Singer's, between the denial of the moral status of non-human animals and racism. Cohen quotes Singer:
The racist violates the principle of equality by giving greater weight to the interests of members of his own race when there is a clash between their interests and the interests of those of another race .... Similarly the speciesist allows the interests of his own species to override the greater interests of members of other species. The pattern is identical in each case.
(NB Singer also makes the analogy to sexism. For the sake of simplicity, I will confine my remarks to the racism analogy. I believe all that follows will apply, mutatis mutandis, to sexism.)
Cohen goes on to argue against this analogy (my emphasis):
Racists ... do grave moral wrong precisely because there is no morally relevant distinction among the races ....
Between species of animate life, however -- between (for example) humans on the one hand and cats or rats on the other -- the morally relevant differences are enormous .... Humans engage in moral reflection; humans are morally autonomous; humans are members of moral communities, recognizing just claims against their own interest.
Elsewhere in the article, Cohen seems to think living in a moral community supervenes on autonomy, and that the ability to engage in moral reflection and act with moral autonomy are one and the same. So I take the central claims here to be that the ability to engage in moral reflection is (A) not a morally relevant distinction among human beings, and (B) a morally relevant distinction between human beings and non-human animals.
Why accept (A)? Prima facie, one might attempt to claim that the ability to engage in moral reflection is an essential property of human beings: if a being does not have this ability, then that being simply cannot be a human being. But as it follows immediately from this that all human beings have the ability to engage in moral reflection, and this is clearly false, this is not a plausible reading of (A).
Cohen himself recognises this problem. However, his solution to the problem is simply to assert (B):
The issue is one of kind. Humans are of such a kind that they may be the subject of experiments only with their voluntary consent .... Animals are of such a kind that it is impossible for them, in principle, to give or withhold voluntary consent or to make a moral choice. What humans retain when disabled, animals have never had.
This appears to be nothing but a non-sequitur.
Why accept (B)? One might, following Kant, claim that the possession of a capacity for moral reflection is the only thing that is good or valuable in itself. Then the possession of this capacity is not just a morally relevant distinction between (many) human beings and non-human animals, but is in fact the only morally relevant distinction one can make in any circumstance.
But Cohen cannot follow Kant down this path. He denies `that we are morally free to do anything we please to animals' and affirms that `In our dealings with [non-human] animals, we are at least obliged to act humanely -- that is, to treat them with the decency and concern that we owe, as sensitive human beings, to other sentient creatures' (my emphasis). He denies, that is, that the capacity for moral reflection is the only thing that is good or valuable in itself: non-human animals have a certain intrinsic moral worth because they are sentient.
With this admission, Cohen not only undermines the classical argument for (B). He also leaves open the possibility that (C) the morally relevant distinction between human and non-human animals with respect to the capacity to engage in moral reflection is overridden by the morally relevant lack of distinction between human and non-human animals with respect to sentience. If (C) is true, then even if both (A) and (B) are true, Cohen's argument still fails: morally speaking, human and non-human animals are more similar than dissimilar, very much in the same way that humans of different `races' are more similar than dissimilar, and Singer's analogy holds up.
Why accept (C)? If the capacity to engage in moral reflection is less morally important than other features, common to impaired humans, non-impaired humans, and non-human animals, then this could explain obligations to impaired humans in ways that imply obligations to non-human animals. Sentience or an ability to reason above a certain threshhold (significantly lower than the classical, implicit standard of a highly-trained philosopher), could be capacities of this sort. This is not yet an argument, but is a line of thought that could be pursued.