1. I live in Kansas City, Missouri. There is a HUGE urban sprawl here. All I could do without one would be stay home. This is the first reason I would have gone with the car. You might live somewhere where this is not necessary.
2. My fondest memories, even the gaming ones, happened with other people. Playing Super Smash Bros. at a friend's house. Driving to the local arcade for Tekken tournaments. Driving my happy ass over to a lan party to play WoW, or Minecraft or whatever. These are just the gaming memories. I also have memories of dates, driving my best friend to school every morning. Ditching class to see Princess Mononoke in the Theater my Junior year of High School. Those sort of things.
3. Money. When I turned 16 the first thing I did was get a job as a dishwasher at a local Mexican restaurant. The pay was slightly above minimum wage, but it covered insurance, dates, games and what have you. Yes you can find a job without a car, but it is harder unless you live in a city with good public transportation or if you live within close walking distance of an employer.
4. Girls. Heh, where would my love life be in High School without the "Dick Tank" (My name is Richard and it was a 1984 LTD Crown Vic. Huge metal boat of a car) From picking up girls on dates to parking on the back roads and unfinished cul de sacs of Raymore I used my car. Quite a few of my first happened in the car, or happened because I had that freedom.
5. The Freedom. I don't know how short of a leash your parents have on you, but within a year of having my car I was working, keeping my grades up and still finding time for Theatre, Choir and Band. They viewed this as maturity and the rest of my upbringing was pretty laissez faire. It allowed my a lot more free reign and I was able to get away with quite a bit more.