Your feelings are based on a few false premises.
First, it is not true that “the younger you start, the younger you will succeed. Starting a business is not like learning how to play chess. The main reason young people have an advantage is that they’re hungrier and more naive, thus being more willing to hustle. The few years it will take you to graduate will not lessen either of those advantages.
Second, it is not true that your parents think you will never be a success, at least it is very unlikely. I don’t want to be presumptuous, because I have never met your parents, but I can confidently say that their desire for you to finish school would not come from this.
Third, the two courses of action are not mutually exclusive. You can start a business while you are in school. Plenty of people go this route and it has the important advantage of leveraging the natural network you’ll make in college. You’ll never find a better place to meet cofounders, and you’ll also be able to meet and date girls too while you’re there, possibly meeting your spouse. All these things become more difficult after you finish school.
Start your business, and go to school. It’s more work, but you’ll be better off.