It’s not that they drain all the happiness out of the world. It’s not that they can’t be killed. It’s not even that they’ll suck your soul out through your mouth if you get too close. Those are all horrifying, but the scariest thing about them, in my opinion, is something that takes longer to sink in.
At least, they are in the books. It’s not really clear in the movies whether they can think for themselves or whether they’re just mindless embodiments of evil. However, in the books, dementors are not classified as a “beasts”. They must be either beings or spirits, meaning they have “sufficient intelligence to understand the laws of the magical community and to bear part of the responsibility in shaping those laws” (Fantastic Beasts, xii). They are capable of some form of speech or communication with humans, having told Fudge that Sirius Black was talking in his sleep, and capable of reaching an agreement with the Ministry of Magic to torment the prisoners in Azkaban and leave everyone else alone. In other words, they have intelligent minds and some degree of free will.
These horrible, happiness-stealing, soul-sucking monsters are capable of logic and reason, fully aware of what they are doing, and completely devoid of compassion or remorse. No other creature in Harry Potter is like that. Merpeople might be creepy, and centaurs cold and aloof, but they’re not monsters. Werewolves can choose to be perfectly good people at any time but the full moon, and humans are a mixed bag, with only a few who come anywhere close to that level of evil. Dragons, basilisks, and most other monsters are basically just highly dangerous animals. But dementors are a horrifying combination of human-like intelligence and cruel, predatory instincts. They really are pure evil, and they presumably know it.