By far the most important factor is that it's flat and population density is high (meaning most bike trips aren't necessarily very far).
An out of shape person riding a bike a few kilometers over very flat terrain is fairly easy, even with a crappy bike. Throw in more hills or longer distances and things change dramatically. Even a single small hill or overpass on a bike journey changes the amount of effort needed by a huge margin and increases the fitness minimum that would result in that journey feeling comfortable.
Outside the cities people still cycle. It is no uncommon for highschool students in the country to cycle over 10 km to and from school (for some up to 20 or 30 km), do the same to meet friends after school, to go clubbing, to go to parties, to go to do things and so on. In the Netherlands there is no such thing as a school bus. There is no driving a car without an expensive and difficult licence after you're 18 years.
And the flatness has a downside too: strong headwinds, always it seems. Certainly, it is easier than riding over hills or mountains, I wholeheartedly agree with you, but it ain't all roses and sunshine either.
Then again, my fitness when I was young was great. Heck, I don't think I've ever seen one of my schoolmates fail the Cooper test during physical education class unless sick or disabled somehow.
Hills: that's not really true if you have a bicycle with a gearing system. You can get a cheap new one with 7 speeds for about the same as a smart phone. That's enough to get past most hills with some but not a lot effort, especially if it's tuned to out-of-shape persons (which modern bikes seem to be). You can always get off and walk the steepest slopes.
There are plenty of other flat and dense places in the world that have almost zero cyclists. It's the infrastructure that makes the Netherlands special.
An out of shape person riding a bike a few kilometers over very flat terrain is fairly easy, even with a crappy bike. Throw in more hills or longer distances and things change dramatically. Even a single small hill or overpass on a bike journey changes the amount of effort needed by a huge margin and increases the fitness minimum that would result in that journey feeling comfortable.