Cats are carnivores. There is evidence to suggest that this is why we have domesticated cats in the first place. Cats and people from centuries ago entered into a partnership to get rid of pests and rodents, since cats like eating rodents like mice and people would rather not have mice in their homes. While they have eventually made themselves cute and fluffy in order to further endear themselves to the people that surround them, being carnivorous is a key component of a cat's existence.
This is so key, in fact, that it turns out a cat that does not eat meat will get ill and die. An Australian couple found this out when they tried to make a vegan cat, feeding it no animal products at all. This naturally did not work, because without meat cats can't actually live, there are components in meat that a cat's body can't produce on its own. As a result, the kitten was near death before being saved by a vet, an essential component of that life-saving treatment being giving the cat some meat that it needed.
The couple who owned the cat didn't want to give it animal products because it was against their own personal beliefs. The problem with this is that their personal beliefs run counter to the way the actual animal lives and what it needs to survive. It is impossible to be a vegan cat because over billions of years cats have adapted to eat smaller animals. As a result, the cat's body is adapted to expect most of its diet to consist of animals, there are dietary components that other animals produce which a cat needs to live. It does not make sense for a cat to go vegan, for it is a born hunter.
People can go vegan if they want to, of course, humans are omnivorous and as a result can go on a varied range of diets depending on what is available. The mistake people make is assuming that all animals are the same, and that what works for man can work for cats, dogs, or other creatures. After all, if a person can be healthy and happy on a vegan diet, why can't a cat?
Well it's the same basic reason you don't really want to feed a cow chicken, it's just not what the body is made to eat. Some animals, and cats are among them, have adapted to very specific diets and circumstances. If anything, a cat's disinterest in most vegetables and plants is another big reason why it got domesticated in the first place. In the early days of agriculture, animals like mice saw big piles of harvested grain and vegetables and thought they were a bountiful food source. People, however, did not want mice eating them. Cats would eat the mice, not the grain, all for a warm place to sleep and a scratch behind the ears. The relationship between man and beast was made possible because it's exclusively carnivorous.
We have gone far from those origins, of course. Better home construction, improved sanitation and more advanced pest control ensures mice are not as big a problem. However, cats are still carnivores, and they still need meat to survive, even if their natural hunting instincts are reserved more for laser pointers than they are for actual animals. To try to change that is to try to go against their basic biology. Yes, a vegan might want to be a friend to creatures great and small, but those creatures are not friends to each other, and it's more cruel to deny one what it needs.