First of all, refer to Kenneth Dover's "Greek Popular Morality in the Time of Plato and Aristotle" (1974) for a classic text on Greek attitudes towards sex.
Thornton tries to demystify quite a bit of popular ideas on what the Greeks thought of sexuality in general and of homosexuality in particular. To be fair, he starts out by saying that 1. He is limited his work to literary texts (because we can't really tell what vases and sarcophagi were meant to say) and 2. He is interested in how those literary texts influenced Western civilization. He argues at the very beginning that the Greek mind had a simple view of the purpose of human intelligence: to impose order on the disorderly forces of Nature. He brings countless examples from philosophy, theater and mythology. Eros was one force of Nature that was as destructive and chaotic as it gets. Eros to the Greeks was a close relative of madness. Hence no surprise that Greek texts treat it like a threat. Sex and violence are tightly related in the Homeric poems and in Greek tragedies for a reason. After all, the whole Trojan war was started by an erotic act. Aphrodite, the ultimate goddess of eros (Eros was her son), was a destroyer. Greek mythology repeatedly points to women as irrational and dangerous beings when they are not humble housewives.
Thornton lives in the age (and in the country) when the state protects against discrimination based on sexual orientation. Much has been written that homosexuality was common among the Greeks and the Romans. Few have had the courage to write the truth: that both Greeks and Romans considered sex between adult males as despicable. The homosexual relationships that were indeed common were between an adult male and an underage boy. Today it's called "pederasty" and it is a serious crime anywhere in the world. It is true that Socrates praises the beauty of men in "Phaedrus", but he is praising the beauty of boys (and in Xenophon's "Memorabilia" he doesn't even seem to approve of physical love). Plato condemns adultery, sodomy and homosexuality as aberrations in "Laws". Aristotle blames the Dorians for having spread the habit to Athens, and it doesn't sound like he was grateful to them for it. The analyses of scholars driven by pro-gay agendas is often selective: it is true that the philosopher Zeno granted equal rights to homosexuality, but he also advocated cannibalism and incest. Weird as it may sound today, pederasty fullfilled a pedagogical function: the older male was supposed to educate the young boy.
The book is a scholarly analysis of Greek texts that leaves little to be desired... except for when Thornton feels impelled to comment on today's (Western) society. Instead of just focusing on the title of his books, he is trying to write a second book between the lines, a book about sex and society in his age. That second book is a lot less interesting and should be left to anthropologists of modern life.