I'm in my 20s now but I decided when I was 15 that I wasn't going to get a license or drive. I wish I'd done it a little differently...you should take drivers' ed and get a license even if you don't get a car. That way you can drive when you carpool with friends which will make things a little easier for you socially, and it's helpful in case anything "happens" when you're out with someone who was driving. Also it will help you understand traffic patterns which makes you a better cyclist. But you don't have to buy a car. I saved a lot of money not having to pay for insurance etc, and that helped me a lot when I got to college.
It was a little hard for me when I was in high school. I felt like there was stuff I couldn't do. But now I think most of that stuff wasn't really worth doing and I had just as much of a social life as anyone who got a car at 16. I never dated anyone who thought bikes were dumb and the one time I went out with someone who thought I was "weird" for not driving it didn't last long. The person I'm with now thinks it's badass that I ride bikes everywhere
Gas will probably never be as cheap, or cars as inexpensive, as it was for your parents. I think people will respect you more in the future for making your own smart choices and sticking to them. Also, if you live in a city--or if you move to one--it will be a lot more "normal" to just walk or take public transit than if you live in the suburbs or a rural area (like I did, everyone drove a pickup). But if you want to make a statement being car-free is a big one.