Contrary to popular belief, dragons are not hatched from eggs. They are born in the same way that humans are, and for reasons unknown to humans and dragonkind, look indistinguishable from human babies. This goes the same for all otherkin. Sometimes it may be the custom for a certain clan of otherkin to mark the child with tribal tattoos, or piercings, or something to single them out as a non-human. But upon arriving from the womb, all babies, human or otherwise, look the same.
In fact, until they hit puberty, there is absolutely no difference between humans and otherkin. Once in adolescence, humans begin developing: girls become women, and boys become men. Otherkin go through a similar process, but with an added phase: they begin to look more like their parents.
Dragons may grow scales, whereas griffins may grow feathers, and unicorns fur and manes. No two otherkin develop at the same rate, or develop the same features in the same order. One dragon may start growing his wings as young as fourteen, while another may not grow her wings until after all her scales had grown in, at the age of twenty. But, sooner or later, all of them looked like their parents.
Their parents didn't quite look like the dragons in books, either. No, they appeared more like humans, just with very convincing stage make-up on, that gave them the appearance of something that was mostly human, with some mythical features. This was the form they used to shop, to go outside, and to live their lives. It was only when they reached this form of half-human, half-other that they developed the ability to finally take the shape of the beasts that they were named after: dragons became dragons, griffins became griffins.
Then, when humans began to go through the second biggest change of their lives, going from adults to elderly people, the otherkin went through their second change as well. However, as humans shrank and developed gray hairs, the otherkin began to grow, and their two forms began to merge into one monstrous form.
The otherkin didn't die of old age like humans, but instead lost their sense of humanity, and eventually had to be put down, for the safety of humankind.
Amongst some dragon circles, this process was often jokingly referred to as a dragon slaying, for obvious reasons. Mostly this phrase was only used by youth, and was frowned upon by their elders. The fact that such a measure was needed was already sad enough without referencing the outdated practice of murdering dragons that was so common back in the days before humans and the otherkin learned to live together.
And so it was that both humans and otherkin learned and taught at Percival Academy, in almost perfect harmony.