With its deliberate echo of the title of Charles Darwin's book The Descent of Man (in which "man" means humanity), Y: the Descent of Men is a study of the biology of men (as opposed to women) and maleness. Y is the Y chromosome, which contains the very small proportion of genetic information that men have and women do not. There is much interesting information, but the lack of structure -- a long series of facts stated one after another with very little to link them together -- makes it difficult to read more than a few pages at a time. Likewise the nudging and doubles entendres rapidly become tedious: for example, when we are told that "man's most basic attribute also has a strong tendency to wilt" we are clearly expected to think of erectile dysfunction, though the context tells us that the sentence refers to the tendency of the Y chromosome to lose genes progressively in the course of evolutionary time.
In the Preface Steve Jones tells that he does not plan to compete with other people with the same name -- the lead guitarist of the Sex Pistols, for example, or the champion golfer, etc. -- but will stick to what he knows, the biology and evolution of males. In genetics his expertise cannot be questioned, but there is more to biology than genetics, and the biochemistry in the book is journalistic in style, with starry-eyed references to "special enzymes" that make oestrogen, nitric oxide, and so on, or "special sequences" of DNA that with affinity for particular proteins. The objection here is to the word "special", which adds nothing because the great majority of enzymes are highly specific (the exceptions are mostly involved in digestion and detoxification, and even these are much more specific than the sort of catalysts used by chemists), and many sequences of DNA are likewise specific: in a world where everyone is exceptional, no one is exceptional.
The editing is often careless, as for example in the passage where we are told (apparently) that Pierre de Coubertin, the founder of the modern Olympic Games, forbade athletes' wives from watching the events, with violations punished by being thrown over a cliff. This is clearly not what Jones meant to say, but only because we know that it is absurd can we deduce what he did mean to say. Or what are we to make of the following pair of sentences: "The lowest [sperm] counts were in Copenhagen, followed in turn by Paris, Edinburgh and Turku (which came a clear top). The citizens of Edinburgh should be proud of their cells' ability to swim, which takes the European gold medal"? Does the author think that Turku is not in Europe? (No, as he told us at the beginning of the paragraph that it was a European city). Is he making a distinction between sperm count and swimming ability? (Hard to believe, as this is the first mention of swimming ability in this context). Why would it be a matter of pride, anyway?
More seriously, the whole book encourages a confusion between maleness and possession of a Y chromosome, even though the author is perfectly well aware (and explains in the first chapter) that the system for sex determination used by most mammals is only one of several that exist in nature. The Y chromosome is slowly losing genes, and may conceivably retain none at all after some more millions of years of evolution, but so what? There is no necessary implication that the male sex will disappear and that humans will adopt parthenogenesis.