I'm at this point in life too, so I didn't really say "everyone should own a car".
A free market includes the freedom to choose the Uber option (given that someone is offering that choice), and private provision of a good means supply is likely to match demand. I'm not against car-sharing - but in the utopian, /r/futurology sort of version of it I sense there are undertones of thinking we'll all be "free" when it's all communal and we don't have property and ownership, plus there's that whole zero-sum view of wealth and prosperity thing.
This "communism will be great when it's Star Trek-type communism" thing is fabulous propaganda. It might not be deliberate or conspiratorial, so propaganda might not be the best word, but that's nearly worse in a way.
I also prefer not to own car as an individual (if not necessary because of lacking infrastructure). It's stupidly wasteful from a monetary point of view to not use the thing most of the time. You have to take care of maintenance and driving in an urban area is also not fun (ok self driving cars would fix this). This "everyone should own a car" as a status symbol thing is/was fabulous marketing.