It’s an easy slide from being part animal to being able to transform between human and animal.
In the West, our minds most immediately go to werewolves: people who transform either into some kind of wolf form, though whether it’s a natural-looking animal, a larger and toothier version of same, or some kind of hybrid wolf-man depends on which werewolf story you’re looking at. The reasons for it vary, too: it’s a punishment for sin, or a product of sorcerous effort, or a disease passed on through being bitten or clawed by a werewolf, or — in modern fiction; I’m not sure this exists in traditional folklore — a matter of heritage, lycanthropy (the Greek term for it) being passed on in a family bloodline.
The origins of this go back a very long way — as in, possibly ten thousand years or more. I’ve mentioned shamanism before; it’s not uncommon for practitioners to take on the spirit of an animal and exhibit its behaviors, and in their visions they may become that animal. The roots of it might be a matter of hunting ritual, praying for help in bringing down prey, and when we see therianthropic (beast-man) depictions in ancient art, it often seems related to that.
Which leads naturally into the idea of shapechanging as sorcery. I haven’t done the research to back up this speculation, but I wouldn’t be surprised if this is actually the most common form of the idea — and in fact it used to be the most widespread explanation for lycanthropy, if you dig back into the older folklore. By putting on an animal skin or a piece of its body, or making a special salve and smearing it over the body, or using some kind of amulet, or otherwise enacting a magical ritual, a person could turn themself into that creature.
The animal in question depends on the local environment. In northern and eastern Africa it’s often a hyena. In Mesoamerica the concept of the sorcerous shapeshifter is widespread, usually discussed under the blanket term nagual; then the animal may be a jaguar, an owl, a dog, a bat, or various other possibilities. At higher northern latitudes, both in North American and Eurasia, you get bear shapeshifters — in fact, the term “berserker” means “bear-coat,” and probably reflects some amount of shamanic-style spirit channeling, but in some variants the warriors literally transform into bears.
When transformation is a punishment inflicted from the outside, it’s often permanent, or at least lasts until someone manages to break the curse. In some instances, though, it’s an intermittent problem, a la werewolves shifting on the full moon. The 1980s film Ladyhawke hinges on a very folkloric motif where someone is cursed to be in animal form either by day or by night. Those of you who are up on your folktales might recognize that as being akin to the Norwegian story “East of the Sun and West of the Moon,” or one of the many related tales out there in different lands.
But some versions of that particular tale-type turn it the shapeshifting concept around one hundred eighty degrees. It isn’t a human cursed to be in animal form; instead it’s an animal taking on human form. Instead of therianthropy, it’s . . . anthrotherianism? (I never took Greek.)
This again has ancient roots. Lots of mythologies feature animals who either married humans, or took on human form themselves so they could, and thus became the ancestors of particular clans. This doesn’t usually grant the descendants shape-changing ability, though, only a spiritual connection or taboos surrounding their relationship with that animal. If you’ve ever watched a bear, it’s easy to understand how they might be thought of as only a step or two away from human anyway.
Animal-to-human transformation is all over the place in Japanese folklore — or rather, yökai-to-human transformation. I’ve mentioned yökai before; it’s a very broad category of supernatural creature, in some ways occupying a comparable role to European faeries, in other ways completely different (starting with the fact that some yökai are humans changed by their own misdeeds — shades of the curse notion above — while others are ordinary household objects that take on a life of their own). One category within that group, bakemono or obake, are specifically shapeshifters.
The most famous of these are probably the kitsune (fox) and tanuki (raccoon dog), but they can also be cats, otters, spiders, weasels, snakes, eels — practically anything, since the underlying idea is that an animal which lives for a hundred years gains magical powers, including the ability to shapeshift. And they don’t just turn into humans! There’s a famous folktale, Bunbuku Chagama, about a tanuki who turns into a tea-kettle.
As with chimerical hybrids, shapeshifters aren’t always dangerous or bad. The ones who found human lineages are of course honored, and while most Japanese stories of bakemono involve trickery ranging from the mischievous to the lethal, in some cases the fox spirits and other creatures get a better rap. The power of shamans is respected — but also feared, as we see with the sorcerer-type shifters. Our old friend liminality is back again: anyone with the ability to transgress important categories like the boundary between human and beast is at best to be treated warily, at worst a threat to be destroyed.
That fear has gotten greatly diluted in modern fiction. Professor McGonagall turning into a cat is a cool trick, dangerous mostly because any witch or wizard attempting to learn it risks screwing up very badly. Werewolves may face a lot of prejudice in urban fantasy, but these days they’re more likely to be the protagonists rather than the monsters the protagonists hunt. Our relationship with the wild is very different from that of our ancestors; we don’t fear being hunted by wolves (or hyenas, or jaguars) on our way home at night, and many of us are at peace with the notion that human beings are a type of animal — thus softening the rigid line between Us and Them.
Besides, I confess. If you gave me some stinky salve or a feather cloak that would let me fly, I would totally do it.