Anthropomorphic fiction is a genre that many writers have explored over the millennia, myself included. Writing with your main characters as animals rather than people can be an interesting, and in some ways even liberating, experience. However, with freedom comes responsibility, and thus there are certain rules that one must follow in order to write anthro fiction well.
There are several things to keep in mind when writing about animals instead of people, first and foremost being they’re animals! This can be a boon to a writer if used properly, but an absolute drag if not taken into proper account. For instance, animals have physical abilities due to their anatomy that humans cannot hope to achieve. Think of a horse’s great running speed or a frog’s ability to leap. There’s no end to the possibilities if you just remember to use your animal characters’ unique physiology. Whereas, if they just act and talk like people, you may as well be writing a boring old people novel.
Another thing to keep in mind is that anthropomorphism has a wide spectrum ranging from feral animals who just happen to think and feel like humans (think Watership Down or Guardians of Ga’Hoole) to essentially upright-walking humans with the mere outward appearance of animals (the Redwall and Mistmantle Chronicles series are good examples of these). Whatever their degree of human-ness, they are going to think and perceive the world differently from real humans because of their unique anatomy and physiology.
Again, take The Mistmantle Chronicles as a perfect example of anthro fiction. Her characters strike just the right balance between animal characteristics (squirrels climb things, otters like water, and so on) and human ones so that they come off as relatable, but still obviously different from us. The same is true in the Redwall series to an extent. Brian Jacques gives certain types of creatures certain proclivities that suit the personalities he gives them. And of course, terminology matters too. If you want to really remind the readers that they’re dealing with animal people, replace words like hands or feet with paws or claws, and remind them of the presence of tails now and again.
On the more feral end of the spectrum, you’ve got to be even more careful to keep in mind the advantages and disadvantages given to the characters by their anatomy and physiology. The rabbits of Watership Down may think and feel somewhat like people, but they are still very much rabbits, and every aspect of their culture and society reflects this, from their dwellings and eating habits to their priorities (mostly involving simple survival) and even the Lapine language they use (which involves a lot of use of the incisors in pronunciation). Lasky’s Ga’Hoole series also takes this approach, reminding the reader that these are in fact owls we’re dealing with a the end of the day: they still fly silently and eat meat raw, however civilized they may act in other ways.
Finally, there is the related issue of to what degree these animals are “civilized”. Do they live a primitive, survival-based existence, or do they have time to build and do creative things? Do they live in natural dwellings or do they construct their own? Have they been imbued with the sense of shame that causes them to wear clothes (and if so, to what extent?), or do they have no such cultural inhibitions and happily go about their business in their natural state? These are all things to think about.
There are many more intricacies to writing animal characters. Too many for a short post like this. But suffice it to say, if you can overcome a few obstacles and keep these simple points in mind, then writing anthro fiction can be a hundred times more fun than sticking with people alone.