I'm sure it has nothing to do with the fact that 78 hours of minimum wage work could pay the rent in 1980, compared to 109 hours in 2010 [1], along with the other associated cost-of-living increases over the last three decades that have come without comparable increases in wages.
I doubt that most people who felt financially secure and could afford a new car wouldn't want to own a new car. Nobody really enjoys driving a beater, or being forced to walk or ride a bike everywhere (aside from doing it for the enjoyment of it), or trying to negotiate for rides with friends. Public transportation in most of the U.S. is awful, so I don't see many people choosing that over having your own shiny new car.
So the article briefly touches on the economic pressures facing young people in mentioning the recession and student debt, but it spends most of its paragraphs trying to paint some kind of cultural picture of "Millenials" as being a neo-beatnik generation that worships sharing.
No, it's the economy, stupid. And not just recently, either; for the last 50 years at least, there has been a gradual trend towards ownership of things like homes and cars costing more and more in terms of the working hours needed to afford them.
If you are among the 3.8 million people making minimum wage (or less!) now [2], a car is the last damn thing you want to own. You won't be able to afford a good one, so you'll constantly be spending money on maintaining it, not to mention that it will strand you one day and your minimum wage job will be more likely to fire you for not showing up than the average cubicle job. Cars are expensive to license, expensive to insure, and in California, old cars are expensive to smog. Even better, if you fail to pay for any of this, you're likely to receive a citation or ticket, which can quickly add up to more time off work and more money out of pocket.
If you're young, you're far more likely to either be burdened by student debts or be making minimum wage [3]. That means that the odds are that you're either not living on your own, in which case a shared vehicle (either a housemate's or a Zipcar or something else) makes more sense than owning your own, or you're living on your own and you can't afford a shiny new Ford Fiesta without a third full-time job.
Additionally, the entertainment industry tends to make more money during economic downturns, and poor people are more likely to spend a greater portion of their money on entertainment. If you can afford little, you might as well have as much fun as you can, especially if your prospects for making more money in the near future aren't that good. If you can hitch a ride to Burning Man, that sounds better than spending the money of the ticket price and time off work and food and everything else on mechanical work for your aging car.
Bah. This article was crap. It didn't have the quality I've come to expect from The Atlantic.
[1]: http://finances.msn.com/saving-money-advice/6952105
[2]: http://www.bls.gov/cps/minwage2011.htm
[3]: http://www.bls.gov/cps/minwage2011.htm again.