Put another way, you cannot educate a child solely by teaching her academic subjects such as math and science. There's more to education than that. That's where sports and extracurricular activities come in. They allow your child to grow. They allow her to be stimulated by new ideas and ways of thinking. They give her a sense of accomplishment and encourage team spirit. These are all excellent lessons she needs to learn in order to be a successful adult.
Let's look at a couple of schools to get an idea of the rich array of choices your child will encounter at private school. Incidentally, it doesn't matter too much whether the private school you are considering is a day school or a boarding school. Either type of private school will offer more extracurricular activities