Before the part of History and Illusion in Politics headed "Human rights" is a part called "Legal rights," which I found very helpful for understanding his later claims about talk of human rights being vacuous, and so on. Here are some of the main points. Geuss sees the modern notion of (subjective) rights, i.e., entitlements or things I can claim as mine, as stemming from Roman law, especially concerning property, by way of the feudal period. Property is linked with jurisdiction in feudal societies, where the lord of the manor might have police powers, for instance, and when we say that we own our own bodies this supports the idea that we have jurisdictional powers over ourselves, and hence moral claims (see p. 132):
The story of the growth of rights-discourse and the story of liberalism are two conceptually and historically diverse stories that touch each other tangentially at various points, until in the immediate aftermath of the Second World War a particular conjunction of the two establishes itself as the ideology of NATO and the United Nations and from that position begins gradually to infiltrate the rest of the world. (pp. 132-133)The idea that we own our bodies is objectionable, but I don't think it's essential to the idea of human rights. Maybe it's tied up with the origins of this idea, but those origins are obscure. In footnote 34 on p. 132, Geuss describes the history of the concept as "infinitely complex." And no strand in this complex web need be regarded as essential, I hope/think/insist.
The original and primary sense of a subjective right, then, is legal. And legal rights are meaningless if not reliably enforced. Hence the need for some mechanism of enforcement. "Failing such a system of sanctions, there is nothing but a set of diffuse individual and collective moral feelings" (p. 138).
I think this is where Geuss turns against rights-talk (wrongly, in my opinion). Moral rights are supposed to be rights, and therefore like legal rights, but they aren't supposed to be legal rights, and they don't even have the enforcement mechanism necessary to make legal rights (actual rights, we might want to say) meaningful. So moral rights are not really rights at all. They are merely moral. This is a little bit like Anscombe's objection to the moral use of 'ought,' etc., so I might be expected to be sympathetic (since I'm sympathetic to Anscombe on this). But what I think Anscombe does is to identify a possible kind of confusion, and one which I think really does exist in moral philosophy. Geuss seems to think not only that talk about moral rights might be, and perhaps sometimes or often is, incoherent, but that it (almost) necessarily is so. He is somewhat cautious in his claims, but not, perhaps, quite cautious enough.
One way to object to Anscombe is to suggest that some or all of the uses of words such as 'ought' and 'obligation' to which she objects might be uses in what Wittgenstein calls a secondary sense. (See here for how to make this kind of objection.) Wittgenstein's idea is very similar to Davidson's ideas about metaphors (see here for more on this, especially the comments by Daniel Lindquist), and since moral rights are supposed to be rights in a metaphorical sense, it seems natural to want to understand them in this kind of Wittgensteinian-Davidsonian way. Anscombe does not explore the secondary sense avenue at least partly, I suspect, because she sees so much (i.e., all) modern moral philosophy as being bad. A meaningful metaphor used to do bad things is no better than a piece of nonsense used to do bad things, so why explore the possibility that the apparent nonsense is in fact a metaphor, even if this possibility has occurred to you? I think there's something similar in Bentham's "nonsense on stilts" rant/analysis: he is as much concerned about the danger of the rights talk he is taking apart as he is about its coherence. And Geuss (at least sometimes) stops short of saying that rights talk makes no sense, and instead tries to argue that it is harmful or dangerous. Given his reference to NATO and the use of alleged human rights abuses to justify starting wars it's not hard to imagine why.