"Humans in furry suits", I think was the quote. Or "humans in animals suits", or something like that. It got bandied around a lot back when I was still involved with the furry writing community. I started to think about it again recently when I picked up a book that's been sitting untouched in my Kindle account for a few years now, one the author advertised and wanted to be reviewed to get it some more attention on Amazon. And no, I shall not slander the author by stating which book.
There's a couple layers to this, I think. The top layer is easy to fix, theoretically. In reading your typical furry story, you tend to run across phrases like this: "He woke up in a cold sweat", or "He pushed a lock of hair behind his ear". In fact, you may notice, you tend to run across these phrases in your typical story, period. They are used as cliche actions that characters make to express emotions without stating them outright. But it needs not be stated perhaps that in typical fiction, the characters making these motions are human.
In this case, let's say the character is a fox.
So, yeah. When would you ever get the impression that either of those two phrases was describing a character who is a fox? Or a wolf, or a bobcat, or an anything other than a human? A horse, maybe, but even then you get this weird picture of a horse lifting up its hoof and brushing part of its mane behind its ear, and... yeah....
Anyway, you get the point. And so authors try to fix this by occasionally throwing out reminders, using 'paw' instead of 'hand', making slant references to fur or whiskers or whatever. But if you don't do that frequently, because the rest of the time you're using these cliche phrases you find in all of fiction that describe humans, the reader easily forgets that these aren't human characters they're reading about, and the sudden reference to a paw is jarring. That's been my experience reading this particular novel on my Kindle.
So, furry writers, please: have more fun with your genre. When you start editing, pull a Thomas Nagel. What does it feel like to be a fox? What is it like physically, and what is it like mentally? How does it influence your personality? You don't sweat; you pant. Your color vision is more limited than a human's, and you're pretty near-sighted, so you don't get quite as much from a beautiful sunset. But your eyes are super sharp at catching motion and act like little mirrors at night. Your senses of smell and hearing are incredible, so you find yourself relying on them more than your eyes. Also, you're not a pack animal: you don't go for the whole 'complex social hierarchy' thing that dogs and primates seem to love so much. Your mom kicks you out of the den when you're a teenager and you have to go find your own little patch of territory, and then later on you meet a lady or a man you like and you stick together for the rest of your lives. You get a rush from killing things, you're cool with nibbling off a rotting carcass, with digging around in the garbage. Sometimes your anal glands really act up and you start to smell worse than a skunk. You get to know who's in the neighborhood by sniffing their pee.
You get the point. This is supposed to be fun, so have fun. And anyway, if you're not willing to try this kind of stuff, then you really have to ask yourself: why not just use human characters? If you can't think of a good answer, then just stick to publishing in places like Weasyl or FurAffinity, because no one else is going to understand the aesthetic.
P.S. And try not to use cliche sentences even if you are writing human characters. This is what I have learned: the fun part of writing a rough draft is plot, and the fun part of editing is language.