The Wizarding World had plenty of Fantastic Beasts, and plenty of intelligent beings who weren't Wizards, too.
The Wizarding World broadly divided its inhabitants—assuming some of them could be called alive—into three categories: beings, beasts, and spirits.
The former Minister for Magic, Grogan Stump, established this definition in 1811. The Being Division then became part of the Department for the Regulation and Control of Magical Creatures.
For centuries before that, the definition of a "being" had been fiercely debated.
From then on, a "being" was defined as "any creature that has sufficient intelligence to understand the laws of the magical community and to bear part of the responsibility in shaping those laws."
Veela, Giants, Vampires, Zombies (yes, Zombies counted as beings; like Vampires, they were undead), Goblins, Hags, House-elves, and Human-Form Werewolves all fell into that category.
When Muggles were being classified, some Wizards argued that they should be considered beasts. In the end, the Ministry of Magic classified them as beings.
Centaurs and Merpeople were widely regarded as beings, but they rejected the classification and declared themselves beasts.
Apart from Veela, Goblins, and House-elves, most of these beings lived apart from others. Most people still couldn't accept them. Though classified as beings, these Demihumans still faced discrimination from most Wizards.
Veela faced the least discrimination of any Demihuman group—perhaps because they were so beautiful. Every Veela who could take human form was female, and every one of them was captivating.
Roger Davies of Ravenclaw could surely attest to that. Enough time had passed since he and Pheobe parted for him to come out from under her spell, only to discover that many of his classmates had made him the butt of their jokes.
To Will, Veela were special for another reason.
Veela and Werewolves were among the few beings