Cats are finicky to the point where they’d rather starve than eat sub-standard food. No matter how you’re feeding your cat, there’s a chance you could be doing it wrong.
For example, most cats are lactose intolerant which means they can’t digest milk. Despite the myth that cats like milk, they can’t digest it properly unless you buy special milk for cats.
Also remember that cats need meat so even if you’re a vegetarian, you may need to buy your cat meat anyway. If you’re a true vegetarian, you can continue eating vegetables but don’t force your eating habits on to your cat.