Wolves are generally accepted as an apex or top-tier predator across cultures and societies. From America to Europe and on into Asia. The genus the wolf belongs to - canis - is also similarly wide-spread with a foothold on pretty much every continent save Antarctica. The genus canis also involves the species of wolves we've come to know as dogs and there is through them a deep and commonly shared heritage of man to animal in human society through a pet-bond, and in many cases the dog is indeed man's best non-human friend.

Now having established that it's then noteworthy that the dog - and by extension the wolf - is notable to across continents and countries of exhibiting a great deal of sociability and almost human traits in the social makeup of groups like wolf packs. It's almost as if the wolf can structure itself as human. It's like the wolf is a human on four legs. They're social, they're intelligent, and they've been a constant antagonist against man among the cultures that matter to the point they're terrifying.

At the final conclusion the Werewolf is the inevitable conclusion of generations of human cohabitation and competition. The wolf isn't just a dumb-ass animal that maybe harasses the sheep at night. It's got enough creative thought in it to make things more difficult. And it can kill, and could kill a man. And if predatory fear of the untamed wolf were to enter the body of the supposedly superior man, then a perfect killing machine is made that can transcend many borders in part because the wolf is so common across many - or all - continents.

Although the werewolf as we know it is descended of the werewolf of pre-Christian Germanic folklore (suggesting in part the infalliable strength and ability of the Germans to fucking drive a hook into everything so it may be carried off by Anglo-Saxon boats into the way-beyond) as a mark of the old-warrior class, there are similar underlying wolf-man mythos abroad which make them more relatable to more people than Asia (which is the only place I know of where the werecat is a thing). Among the Turks and per Tengri beliefs the Turks believed that pre-Muslim shamans would assume the form of a wolf after rituals. Native Americans have their own werewolves, with the Naskapis beleiving the Caribou afterlife is guarded by wolfman spirits who kill way-ward hunters and the Navajo myths of the Skinwalkers puts the demonic shape-shifters into a wolf-form.

Similarly there's folktales in Northern Africa from Ethiopia to the Berbers of Morocco of a class of people possessing the ability to change into a hyena - a relative of the wolf - at will. This being called the Buda.
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Lions, tigers, and other big-cats aren't nearly as wide-spread as the wolf or often as close to humanity as the wolf. Likewise as said before, big-cats are considered the realm of the modern furry. The canine is more the realm of classical anthropomorphic ghost stories.