Do people really not keep their cars that long?

The reason I ask is because my grandma (who has a pretty old car, a 1999 Ford Taurus) says that most cars on the road aren't that old and that most people get a new car every four years. I'm about to get my first car and when I told her I was thinking about getting a used car (like a Honda Accord, Nissan Altima, or Toyota Camry) and I told her it would be about 12 years old or so she said that was too old and that it would start breaking down. What's wrong with getting a car that old? Some people tell me a reason for her view is because she always mainly owned American cars and isn't really aware of the reliability of companies like Honda and Toyota. However, I know that any Accord, Altima, or Camry is going to last longer than a Taurus.

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