There are so many different types of tires because there are many different types of cars and many different preferences held by those cars' owners. When selecting between different tire variables -- sidewall height, tire width, compound and tread -- there are inherent trade-offs that make lots of choices necessary.
The first trade-off faced by consumers is performance versus price. Generally speaking, a higher-performance tire is going to cost more money. Performance, however, means many different things to different drivers. A sports car owner is likely to favor greater grip at high speed and the shortest possible braking distance. In exchange, these tires are likely to wear out quickly, create lots of noise and transfer motion to the car.
A suburban parent is likely to favor a quiet, smooth ride. In exchange, these tires are likely to perform sluggishly and not allow for high-speed maneuvering. A commercial driver is likely to favor economy over all else. In exchange, these tires are likely to perform poorly, create lots of noise and transfer motion to the car, but they are also likely to have an extended lifetime mileage.
Meeting the needs of these different customers, with all the different cars they drive, means tire manufacturers need to create a lot of different tire sizes and types. For each of these customers, variations must be made in tire dimensions to deliver the needed performance at the best price.