Omnivores can live on veggies; however, maybe not the healthiest diet.
Look at a cats teeth. Those are strictly for a carnivore.
The only way a omnivore can live healthily on vegetables alone is if they supplement their diet with foods that are not found in their local environment. The same holds true if they eat a totally carnivore diet, but in that case they would have to eat organ meats that most people can’t (or won’t willingly) eat to get the nutrients that are not present in the muscle fibers they eat normally.
Cats are obligate carnivores, they can and sometimes do eat some vegetables (I have a cat who adores mushrooms fried in garlic and butter) but they can’t digest them well, and they do not get the nutrients they need from them.
Cats are carnivores.