It's a show about a snarky, rude loner who doesn't even bother trying to fit in. Supernatural weird things happen. Girls need help. It's based on a light novel series. There are other examples of this genre.
However it also happens to be excellent.
What's different about it, I think, is its willingness to embrace family-unfriendly sentiments. "Just be mediocre. Don't try to do things you can't." "It's okay to hate yourself." Our dead-eyed protagonist, Sakuta Azusagawa, couldn't be further from the usual inspirational cheerleader one expects in fiction. He'll say slappable things to people's faces, often about sex, personal comments or his own selfish desires. (It would be possible to play this with a twinkle in one's eye and turn it into flirty leg-pulling, but the character's delivery is too cold for this even when the actual dialogue is obviously flippant. "Your girlfriend picked another fight with me yesterday. You really have to choose between me and her." He's clearly doing it deliberately, but it doesn't land well.)
His manner isn't lovable, to put it mildly. However he does have the ability to accept people as they are, without fuss or moralising. He helps them. He's not fussed even if they're turning invisible, they're an eccentric interpretation of Laplace's Demon or they're having split/swapped body problems. After all, his own life's worse. He has a little sister who at first looks like a silly anime stereotype, but in fact really, really isn't.
It's intelligent. The cast are sensible and level-headed, while also still having feelings. They also have intriguing, self-aware conversations. The show's liable to feel like an exploration of high-level quantum physics, while also being about, say, social exclusion due to both the butterfly nature of celebrity and also the groupthink of the classroom herd. It's honest in its exploration of some regrettable, contradictory feelings about friends and family members. Some of the sentiments expressed might make you blink. You don't often see things like that being said.
I thought all that was excellent.
I like Sakuta. "It's hard to handle trouble when no one believes you." He accepts big things so unconditionally that he's capable of being shocking in how far he'll go in this. When Kaede declares her intention to SPOILER, for instance, he doesn't cheer her on. He tells her not to, saying that she's being too ambitious and trying to do too much too soon. He helps people with some pretty serious issues. He says offensive things, but pay attention to the one person to whom he doesn't. And then there's where he goes emotionally in the last few episodes.
I like Mai. Their romance feels real and intelligent in a way that feels earned, with their personalities that genuinely belong together and plenty of things to work through. They can seem cold, but you'll also see what's underneath. The show's also found a plausible, interesting way to justify a steady girlfriend/boyfriend relationship that nonetheless fits around a series structure of "impossible things happening to the latest emotionally messed-up girl of the week".
It's a strong show. It's also good fun, in its spiky, Fortean way. It's got hospitalisation, magical injuries, scarring and quite a good (if deadpan) sense of comic timing. I admire it. It was capable of shocking me. There's a 2019 movie sequel and I'm definitely watching that too.