Just a few stabs at a possible answer:
Fuel tax is MUCH lower. Not just aviation fuel, all fuel.
It's one culture and language througout the continent. Travel is much more common.
There's far more free space on the surface. Places are farther apart. This means that the airspace above is far less crowded and thus easier to divide.
Most airfields are owned by the FAA and included in aviation fuel is a surcharge for use of FAA facilities like ATC and airfields. Thus no landing fees.
The Americal culture has more admiration for high achievers, whereas in Europe, when you do something extrordinary (like getting a pilots license and a plane) you are seen as a snob or a showoff or something. So if you get a PPL and your own personal airplane in the US to beat the traffic or travel for business, people will think "that's clever", whereas in Europe they'll call you a showoff or something.
After WWII, most of the industry throughout Europe was wrecked and needed a long time to get back to speed in producing essential stuff. At the same time in the US, the war industry was fully ramped up and looking for war-like stuff to produce for civilian use. Cars, motorbikes, airplanes and such were very logical.