As many have said anthropomorphic animals aren’t same things as furry animals. The groups overlap sure but have some important differences. Furries are mostly self and sexual expressions thing, where as antros are story telling and character creation tool.
Animal motives are found all over the world and all genres of stories. While there are multiple different uses of animals in stories, the most common is using animals to get a mood or ability across. Human have always connected some symbolism to animals usually trough their place in food chain, visual element or distinctive skills. There is reason why many gods have animal parts or animals closely associated with them. Want to make something look strong and dangerous, use large predators like bears, tigers and sharks. Want make something look cute and innocent, use small mammals like mices, bunnies and hedgehogs. Something fast, horses, hawks and cheetahs. Something wierd, insects, octopuses and snakes. Cunning, cats and foxes. Dirty, pigs and rats. Beautiful peacocks and butterflies. Loyal, dogs. We have large library of these and they work pretty well even across cultures.
Despite the rich symbolism actual animals are limited at their story telling potential by the fact they don’t talk, built things or behave like humans do. So they are presented more human to be allow more stories, often to a point acting just like humans. Then you might ask why use animals at all, why not have just an animal t-shirt for the mood setting? People have certain distance to animals so have larger window for willing suspension of disbelief with animal characters than human characters. A fun story that would feel too stypid with people can work out with animals just fine. Story that would feel too dark and disgusting can be easier to approach with animals. Plus people of all sorts find amusement when animals behave or are presented in unusually human manner. There are Victorian era photos and taxidermies of kittens in clothes.