(1) was it homosexuality or bisexuality? It is questionable whether the distinction between the two even makes sense in an ancient Greek context

(2) it was socially acceptable for a grown man to have relations with a teenage boy, but a grown man having such a relationship with his social equal (another free adult male) was (generally speaking) viewed much more negatively; by contrast, in the contemporary West, the former is increasingly viewed as taboo, the latter as increasingly acceptable, which is moving in the complete opposite direction to the ancient Greek attitude

(3) the term "homosexuality" encompasses both male-male and female-female relationships, but ancient Greeks didn't treat them as equivalent: in many city-states, the former was much more socially acceptable than the latter (Sparta was a noticeable exception, possibly due to its more egalitarian gender relations). Many cite Aristophanes' speech in Plato's Symposium as one of the few ancient forerunners of the modern homosexual-vs-heterosexual distinction, yet it treats female-female and male-male relations as two separate categories, rather than merging them into a single category of "homosexual"

(4) contemporary Western ideas tend to emphasise heterosexual and homosexual relations as interchangeable and equivalent; ancient Greek views did not. Many ancient Greek men had both a wife and an adolescent male lover, but we have no evidence any of them ever thought of marrying the latter. They wouldn't view the two as coequal members of a common category, as much contemporary Western thought does

(5) the idea of sexual orientations ("homosexual", "heterosexual", etc) as categories of persons was largely unknown in the pre-modern world. As I mentioned, Aristophanes' speech in the Symposium is sometimes viewed as a precursor of that modern idea, but (a) the Symposium is arguably not representative of the mainstream of ancient Greek thought on this topic, (b) given it is a speech by a comedian in a text rich with irony, it is unclear how seriously Plato actually wanted us to take it (c) in the details it doesn't agree with modern concepts either (missing any concept of bisexuality, and treating male-male and female-female relations as two separate categories on the same level as male-female ones)

> or why you're putting scare-quotes around it

To emphasise its status as a word (and the specific concept/cultural construct that word represents), which emerged in the context of a particular culture and historical period, and hence whose applicability to very different cultures in very different historical periods is open to question

> Anything involving sexual relations between men is anathema to Christian conservatives.

I don't see how the views of contemporary Christian conservatives has any inherent relevance to the question of how applicable the word "homosexuality" is to ancient Greece

Modern high culture is what, 2 centuries old? Maybe 3 in Paris and parts of Italy? And modern embraceness of homosexuality barely 50 years old?

Whereas Greeks had at least 5 centuries of high culture to perfect their "craft".

If you are defending the "modern homosexuality" specifically that stops looking like Human Rights and starts looking like a fad.