There are several main obstacles:
1) The Gubmitt - Moller has been trying to get his Skycar approved by the FAA since I was in high school, 40 years or so ago. He is still trying...
2) The Gubmitt - The FAA stupidly cites an overwhelming demand for air traffic controllers should lots of people get Skycars - the typical Gubmitt centralized command & control paradigm. If we had the huge Federal government of the current day back when the Model T was first invented, we would all be riding horses - and shoveling up after them. "Global Warming" would be mainly blamed on Methane rather than CO2 - Methane being emitted from that part of a horse's body that is clinically indistinguishable from the average Gubmitt bureaucrat.
Put collision avoidance on the CAR, not a central point on the ground! This is easier than doing it for a ground car - you have three degrees of freedom, not just two (and sometimes only one [faster/slower]).
Microcomputers have come a long way since 1975 - each car could exchange packets and agree on which one goes up, down, left, right, faster, slower... Things like "sparrow-flutter algorithms" could be implemented allowing your car to join a flock - the possibilities are vast and far beyond the capacity of the typical FAA bureaucrat's imagination.
3) The Gubmitt - The Federal and State Governments have glommed onto the lion's share of the airspace over the United States, placing classified and sensitive facilities in a geographically strategic manner, allowing them to restrict air travel in most of our sky. Flying cars would make what they are up to painfully obvious to the bulk of We the People, not just those few who actually fly small planes - and the Gubmitt would rather avoid that contingency.
4) The Gubmitt - County and Municipal Governments base their property taxation systems on street addresses - no roads, no street addresses. If the flying car took off they would have to work for a living and come up with a new system based on Geocodes or GPS coordinates for example.
5) The Gubmitt - Roadblocks are a tough job when there are no roads - pretty hard to restrict vehicular mobility in the sky using your vehicle - and tire spikes are just no good at all. Given the necessity for sophisticated electronic systems in order to put collision avoidance on the Skycar rather than on the ground, the law enforcement agent could simply be given the capability to control your Skycar remotely - but people would likely find ways to defeat any such system. Law enforcement would really hate that...
6) The Gubmitt - There are a lot of toll roads in this country - many of them paid for several times over. Lately State governments have been selling these off to foreign interests for a bucket of cash with a helping hand from the Federal government - and these foreign interests then proceed to charge us to use roads that we had already paid for but now are expected to do so all over again. The ubiquitous use of flying cars would snatch this little sugar-plum right out of the Gubmitt's greedy little sausage-fingered hands - and it is not OK with that.
7) The Road Construction Industry and its associated suppliers - Roads cost a lot of money both to construct and to maintain. It is a good-sized chunk of state and local economies. There is a large industry that has grown up to serve this market - and they employ a lot of people. If the flying car took over (and it would, if it were done well enough), this industry would be devastated and a lot of people would lose their jobs - similar to what happened to the blacksmithing and buggy-whip industries when the automobile caught on.
8) The Trucking Industry - If the flying car took off, taxation of gasoline and such in order to maintain the roads would become difficult to justify. The remaining constituency using roads after the majority of us went flitting of into the sky would be truckers hauling heavy freight that would be technologically infeasible to move by air to locations like warehouses and construction sites.
Rail and river barges could get it to the depot, but getting it from the depot to the point of use would be an issue if there were no roads. The trucking industry would have to bear the lions share of the road maintenance burden - which would render that industry economically infeasible, since they would have to pass the added financially significant expense on to their customers. It would soon get unreasonably expensive to transport heavy items to the locations where they are needed, and the resulting economic dislocation would be painful for everyone.
This last one is a tough nut to crack, unless new technology, such as anti-gravity for example, becomes generally available.
I personally want the flying car rather badly. I hate roads. The entrenched road industries consume significant recurring expenditures that are largely financed through taxation. These industries tend to be bastions of city council and county commissioner "Old Boy Network" chronieism, encouraging influence peddling and nepotism. Roads are what give Human civilization the appearance of a staff infection on the face of the Earth when seen from above.
It would be so much nicer to see a forest with little clearings in it for the houses and no nasty black/grey/white lines running everywhere. No nasty grids of close-packed Man-Hiveage, with all of the houses all lined up looking like an array of Chicklets from the air.
I'd even put up with a few beer-cans on my roof if it meant that I could fly my car like a bird...