Cats are obligate carnivores, meaning that there are certain nutrients they cannot get from any source other than meat.
An example is taurine. Without taurine, a cat can suffer blindness. While there are some felines raised on a vegetarian diet (using a synthetic taurine supplement), the vegetarian diet is not natural to felines, and requires a lot of research and great care to get it right.
Another consideration is that a cat on a vegetarian diet is quite likely to seek animal based protein from elsewhere.
Nutrition is an important consideration for a growing animal. And any nutritional deficiencies in kittenhood may cause problems further down the track.
While it's not impossible to bring your pet up as a vegetarian, it certainly isn't a natural state of being for a cat, and its health will be compromised over the long term. It is a huge decision that should only be made with veterinary guidance.