HOKAY. And I say this as someone who is getting her PhD in animal nutrition, and who has taken specific cat/dog nutrition classes: their bodies aren’t built for it, especially in cats. Dogs will be malnourished and unhappy on vegan diets, but cats will outright die of malnutrition.
In the wild, while dogs are more omnivorous than cats, the majority of the canine diet came from meat (fun fact: in dogs, the molars are shaped to allow for crushing and grinding, primarily of not plant material like ours, but of bone/cartilage/viscera. When a dog chews a bone, it’s the molars it chews with). Cats? Plant matter comes in the form of whatever their prey had in its belly. Cats and dogs will self-medicate with plants, but that’s mainly to induce vomiting/calm upset stomachs.
In addition to teeth, look at the intestine:body length ratio. The larger that ratio, the more herbivorous the diet is. (Longer intestine -> larger space for complex carbohydrates to be digested/carbohydrate-digesting bacteria to camp out in).This has been shown across taxa, from mammals to birds to fish (sample reference: http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2435.2009.01589.x/pdf ) Cats = 2.5:1, dogs = 3-4:1, depending on breed (source: http://www.amazon.com/Nutrient-Requirements-Dogs-Domestic-Animals/dp/0309086280/ref=sr_1_1?s=books&ie=UTF8&qid=1389829146&sr=1-1&keywords=0309086280) Humans? 10:1. Ruminants and horses have even higher ratios (see http://www.ag.auburn.edu/~chibale/an02physiology.pdf ) Cows, for example, have a 30:1 ratio. Horses are 15:1.
Cats and dogs also have much more concentrated acids in their stomach, and a higher amount of proteases (enzymes designed to cleave proteins apart so that they can be absorbed) and a lot less of the amylases needed to break down carbohydrates. Because of the short intestines relative to body length, cats and dogs have a higher passage rate (ie, food stays in the gut a lot shorter) - this means that their diets favor highly digestible foodstuffs like proteins, as opposed to complex carbohydrates, which take longer to digest and absorb. Many plant proteins are also bound up in complexes that require specific enzymes that cats and dogs don’t have. (Look up phytate/phytase sometimes and why that’s a big problem for high-soy diets). So high-carbohydrate diets pass through the intestines too quickly for the carbohydrates to be properly broken down and absorbed, and basically result in a lot of poop, but not much nutrition.
Now let’s look at where we get energy - everything has the same basic requirements for protein, glucose, water, minerals, vitamins, etc etc etc, just in varying amounts. But every species is different in its preferred form - some animals preferably use carbohydrates for glucose (horses/rabbits/guinea pigs). Most carnivores, however, prefer protein, and their bodies are optimized for it. In carnivores like cats and ferrets, their main source of energy (glucose) is gluconeogenesis, that is, making new glucose from non-glucose substrates. Obligate carnivores like cats and ferrets are VERY efficient at this, and their ability to digest carbohydrates and get glucose that way is really quite limited (cats aren’t eating much carbohydrates in the wild, so cats that couldn’t digest carbohydrates well but did digest protein well and had good gluconeogenesis survived to reproduce).
In humans, the gluconeogenic cycle can be turned on and off in the liver, depending on energy levels and our diet - in cats, it’s always on. Because of this, their body preferentially burns protein for fuel - and it needs to be easily digestible protein (like in meat). If they don’t get enough easily digestible protein, the body will start burning its own muscle protein for energy. Dogs are not quite as bad as this, but they still have incredibly high levels of gluconeogenic activity compared to humans.
There’s also the problem of essential nutrients - essential nutrients are nutrients the body cannot synthesize from other substrates. For example, humans (and guinea pigs!) have vitamin C as an essential nutrient - we lack the L-gulonolactone oxidase enzyme needed to synthesize it. While humans only have 10 essential amino acids that we must get from our diet, cats require an eleventh: taurine. Taurine in cats is needed for proper heart/eye/digestive function. Without it, cats will die (in a very painful manner), and it is found only in animal proteins. If a vegan cat food has taurine, it’s not vegan - that taurine was isolated from animal protein.
Cats also need arachidonic acid, which is only found in animal products. Most animals can synthesize it from linoleic acid, but because cats in the wild get such high dietary levels of arachidonic acid, cats that couldn’t synthesize it were still able to survive and reproduce successfully. Without arachidonic acid, cats suffer from painful skin/gastrointestinal/blood diseases, and will die.
Dogs and cats also have an absolute vitamin D requirement - they cannot synthesize it in their skin like humans. The most bioavailable form, D3, only comes from animal sources. Dogs can use D2, but it’s very inefficient and can lead to vitamin D deficiencies. Cats cannot use D2 and have an absolute requirement for D3.
A dog on a vegan diet will most likely suffer from a lack of protein and essential vitamins. A cat on a vegan diet will die. For the best health outcomes, you should feed your cats and dogs a high-protein, low-carbohydrate diet. Taste of the Wild, Blue Buffalo, Nature’s Variety Instinct, and Back to Basics (dog food only) are brands I personally recommend (as did my professors at ISU)
I have no problem with humans being vegans, as long as they’re making sure to get a good balance of nutrients. It’s not for me (violent soy allergy, for one), but if it makes you happy, that’s fine. Humans are omnivores - we can do fine on plant-based diets. Dogs and cats can’t. Don’t adopt a carnivore and try to force it to be a herbivore - do your pet a favor and get one of the many cute herbivores (rabbits, guinea pigs, a lot of birds, most rodents) that do just fine on a vegan diet.
I hope that answered your question, anon.