Cats can't digest carbohydrates. Their biochemistry doesn't have a way to convert carbohydrates into energy. All cats can digest is protein and fat. That means all of their food must come from eating animals. When you see cats eat plants, it's for roughage, for the fiber, not because it gives them any nutritional value or energy. In fact, the fact that cats can't digest carbohydrates and that many cat food manufacturers put carbohydrates in cat food at filler because it's cheaper than meat is why dogs eat cat box crunchies out of cats' litter boxes, because it's food, because all the carbohydrates just pass through their digestive system making their poop high in carbohydrates, which unlike cats, dogs can digest.
Why do tigers have sharp teeth? Evolution. Because they evolved to be strictly carnivorous and need those sharp teeth to kill and eat their live animal pray. Tigers would not survive in nature otherwise.
By the way, tigers have muscle density that is nearly six times the muscle density of human, more that twice the muscle density of lions. That means that if you have a one inch by one inch cube of tiger muscle and a one inch by one inch cube of human muscle, the tiger muscle will weigh six times more. That's one reason tigers have so much advantage over lions in a fight. Not only are tigers larger than lions, but even if you take an adult, male lion that weighs about 300 to 400 lbs., if you find a small tiger that is about the same size, meaning the same in height and length, the tiger will look skinnier than the lion, so you might presume it weaker, but it will actually weigh over 600 lbs.
That extreme muscle density that tigers have is owing to their carnivorous diet. If you tried to turn a cat, tiger or otherwise, into a vegetarian, depriving it of all meat and meat protein, it would die of starvation. You could be feeding it hundreds of pounds of fruits and vegetable a day, but it would still starve to death because its body in incapable of converting the calories in fruits and vegetables into the energy it needs to live.