I don’t think owning a car is necessarily a problem. For me FuckCars mostly means “fuck using a car unless you have to”, which means using a car for those kind of commutes that people do every day or very often. Go to your workplace, school or university, go shop groceries…
There will be other context where you are going to need a car. Your holidays, for one. It’s not a problem in my book. And of course it also applies to a lesser extent to folks living in the countryside, where it’s inherently more difficult and expensive to link communities to transit. Our main concern should be ridding cities of cars and you guys in the Netherlands are already doing an amazing work on that front in many places.