(Edited to add: Apparently, there was also a backlash on the grounds that the age gap between the main characters was off-putting to many viewers, but I was unaware of this before it showed up in the comments to this review).
Which is a somewhat silly question, on account of it having at least one absolutely pragmatic reason (ejaculation and erections are both instant triggers for an NC-17, and why needlessly crush the film's box office prospects?), and one more esoteric, artistic reason: this isn't a film about sex, gay or any other sort, not really. It's a film in which gay sex is symptomatic of the actual content, which is the shyness and uncertainty of first love; specifically & necessarily same-sex first love, but not just because of the fucking.
The thing is, Call Me by Your Name is a film directed by Luca Guadagnino, who has already made quite an estimable career as a sensualist; his films are horny as hell, but they're not horny for genitals and orifices. They're horny for beauty, textures, experiences; I Am Love (his 2009 international breakthrough and his best film to date) is, to me, a film about the stimulating beauty of food, and while 2015's A Bigger Splash is very invested in the sexiness of its four leads, it is more invested still in the sexiness of how the white sunlight reflects off the turquoise water in a swimming pool. Call Me by Your Name is really just the natural progression of this fascination with surfaces: after two wonderful features of being turned on by the erotic charge of colors and textures, Guadagnino has made the obvious leap to reapply those colors and textures to human flesh.
And there is lots of human flesh. Set over the course of summer, 1983, somewhere in rural Italy, Call Me by Your Name starts its sensory overload by presenting most of its male characters in a perpetual state of shirtlessness, and its female characters in bikinis, all to suggest the humid cool of being thus dressed-down. Also because it is a film terribly much taken up with the notion that looking at barely-dressed humans is pleasurable; and this is another way in which it's not "about" sex, but about the anticipation of sex - about the visual stimulation of seeing beautiful people close enough to naked that they're practically demanding you to visualise the rest of their tiny clothes off. And this stimulation proves to be a hell of a lot for 17-year-old Elio Perlman (Timothée Chalamet), whose academic parents (Michael Stuhlbarg and Amira Casar) own a beautiful estate where they visit for summer and winter holidays, hiring a graduate student to help Mr. Perlman in his archaeological studies for the summer. In 1983, that student is 26-year-old Oliver (Armie Hammer), and the film documents the achingly slow process by which Elio figures out the vocabulary by which to tell Oliver without telling him that the teen has a gigantic crush on the visitor; and then the nervous flirtation that emerges between the two of them; and then the very enthusiastic physical relationship to follow.
It's all very small-scale stuff: a "what I did on my summer vacation" essay about first love, first sex, and the giddiness of watching the person you're infatuated with go about the fascinating acts of e.g. reading a book or taking off his shoes. But the smallness is exactly its strength: this is as good a depiction of teenage lust, both physical and emotional, as I can remember seeing in God knows how long, in large part because of how much both the native state of nervous,shy, infatuated teenagers and the filmography Luca Guadagnino is an intoxicated state of looking-at-the-thing. And he's got a hell of a partner in crime this time around: the film is his first collaboration with Sayombhu Mukdeeprom, who shot the unbearably beautiful Blissfully Yours, Syndromes and a Century and Uncle Boonmee Who Can Recall His Past Lives for Apichatpong Weerasethakul, and the images in Call Me by Your Name are the best possible middle-ground between their respective filmographies. From Guadagnino comes the luxuriant focus on textures interacting with each other, be it cloth-on-body, water-on-body, peach-juice-on-body, or even non-body imagery, like water on rocks and books on shelves. From Mukdeepro, comes the diffuse lighting, creating a fuzzy, dreamy state of being in nature as an unreal haze.
The net effect is a film that's ravishingly pleasurable to look at purely as visual abstraction, even before we get in the business of the erotic depictions (and there are both wildly objectified male and female bodies, so as much as the film is invested in the male-on-male gaze, it's leaving something on the table for straight dudes and lesbians). Not that it's necessarily more beautiful than Guadagnino's other films, which have set a very high level for visual beauty; and while Chalamet and Hammer both turn in very fine performances (I'm especially fond of the way Hammer moves: lazy poses that suddenly coil up and turn into darting motions, like a happy rabbit jumping from place to place), it lacks the strong human element of his collaborations with Tilda Swinton (who has held the lead role in three of his four previous features). Still, this is a rich feast of simmering adolescent feelings, visual celebration of human and non-human beauty, and a lazy pace that evokes the hot-but-not-too-hot relaxation of the Italian summer.
So with all that in place, now I don't feel bad about saying something really shitty about the film: it has awful editing. Not persistently, and not enough to ruin the movie. But certainly, there are many jarring mismatches of body position right exactly where our eyes want to go, and enough points where the movement and camera angle jam against each other all wrong, and one fucking bizarre moment where a two-shot of Stuhlbarg and Hammer cuts to a different two-shot of Stuhlbarg and Hammer, in what is obviously an attempt to use the best line reading with absolutely no fucks given about the visual rhythm. During Stuhlbarg's big summing-up-the-film monologue at the end, there's a big ol' wallop of a continuity error that comes real close to sucking the wind out from what very well might the film's best scene otherwise. Again, this doesn't ruin the film, but it happens often enough, especially at the start, that it kept me on high alert. I won't name the editor to shame him, because this looks very much like a best attempt at dealing with problems in the footage; but the problem remains, a hideous blemish on the movie's perfectly-sculpted surface.