So, I've only skimmed the book, but here are my thoughts. The debate about whether sex is binary or a spectrum is not really worth a whole book. In fact it's not really worth a whole chapter. Sex itself is a fascinating topic in biology and the popular literature and the 'hard research' is inexhaustible, but the concepts and mechanisms of sex are so well defined, and the binary categories are so obvious that there has never been a scientific debate about the its existence or relevance. Indeed the only interesting discussion is in evolutionary biology about why the large gamete/small gamete system is so uniform across complex life forms and why alternative strategies did not evolve. The basic, though speculative and contested answer, is that the cost of sex in term of reproduction is enormous. Asexual reproduction is vastly more efficient. But sexual reproduction confers one benefit that is essential to complex life, meiosis -- the ability to mix and match parent genotypes and therefor provide a genetic mechanism for evolutionary adaptation. Biway meiosis and large gamete/small gamete (biological sex) reproduction confers such a huge advantage in itself and is so adaptable, that alternate, more complex (and thus even more costly) schemes always result in evolutionary dead ends.
Seen in this light, the binari-ness of sex is not a scientific debate and therefor can't be argued from a scientific perspective. What has really happened is that a new concept, sociological sex, has been invented, and given a technical meaning, and that concept has been conflated with the commonly used term 'sex' and therefore with what must now be called 'biological sex' to disambiguate it. Since you're entering the realm of defining the terms of the debate, shared understanding and the definition of things (with a healthy dose of obfuscation), this is a debate that can't be 'won', all you do is describe what the gender ideologists' gambit is and to understand its history, context, and motivation.
To his credit Elliott provides considerable details on both aspects, scientific and sociological, and from that perspective is useful. But "debunking the sex spectrum myth" is a Quotidian quest. In the Popper sense, the concept isn't even debunk-able (falsifiable), except in the sense that it's self-contradictory.
I think Joyce's Trans is a better book for understanding the practical contours of the debate as it presents publicly in trans rights advocacy. She summarizes it succinctly as four arguments used to make the case sex is a spectrum:
- Binary sex is an artefact of Western colonialism.
Answer: "such third genders have no bearing at all on these traditional societies’ understandings of biological sex. They are, rather, testimony to the rigidity of their sex roles: a way to prevent effeminate, same-sex-attracted males from sullying the class of men."
Answer: "Since clownfish can change sex – or, more generally, that since not all living things are sexually dimorphic and incapable of changing sex – there can be no objective distinction between male and female. But you need a definition of male and female to observe that clownfish can change sex – or that some other living things are hermaphrodites, or reproduce asexually – and you will then be able to see that sex in humans is indeed binary and immutable."
- Disorders of sex development (DSDs), i.e. the intersex conditions trope.
Answer: "As with any part of the body, reproductive organs may develop in anomalous ways, just as some people are born with extra fingers or toes, or missing eyes or legs, but humans are still ten-fingered and ten-toed, binocular and bipedal. For there to be even three sexes there would have to be a third gamete, and there is not."
- Sex – not gender – is socially constructed.
Answer: "A remarkable example of deconstruction is provided by the definition of ‘female’ proposed by Andrea Long Chu, an American transwoman and author of Females: A Concern, published in 2019. ‘Everybody is female, and everybody hates it,’ writes Chu. ‘Femaleness is a universal sex defined by self-negation . . . I’ll define as female any psychic operation in which the self is sacrificed to make room for the desires of another . . . [The] barest essentials [of femaleness are] an open mouth, an expectant asshole, blank, blank eyes.’
"This definition is obviously influenced by pornography (and Chu has written that ‘sissy porn did make me trans’). It is striking that receptive anal sex, which is possible for people of both sexes, is the act that Chu regards as defining females. If you actually are female, it is also highly offensive – and would be incomprehensible, if you did not understand that the aim is to enable males to count as females. Deconstruction is supposed to free the members of a subordinate class from subjugation within a binary – and I suppose it does, in a purely linguistic sense. But it is freedom at a high price: denial that the subordinated class even exists in any clearly defined way.
"It is all an immense pity, because there is a concrete sense in which deconstructing binaries could be liberatory. As Simone de Beauvoir explains in her classic The Second Sex, published in 1949, patriarchy centres Man and defines Woman only in relation to him. This value-laden binary is reinforced by many others, including subject/object, order/chaos, active/passive, strong/weak, reason/emotion and light/dark. Feminism is the task of centring Woman in her own life, and unpicking these associations. In the binary reason/emotion, for example, emotion is both taken to be inferior to reason because it is Woman’s domain, and taken to be Woman’s domain because it is inferior to reason. Feminists reject both propositions. A rounded life requires both, and neither need be the domain of one sex or the other."