I believe that the transition to self-driving cars in some ways will mirror going from the horse-and-carriage to the modern car.
Many people in the early 1900’s didn’t care for the automobile as it was becoming more popular, they preferred horses or walking. Eventually it became cheap enough for the common person to own one and the utility over the horse put horse-riding out of style. The car was faster, stronger, and easier to maintain. Of course horses are still used for recreation and sport, and you can hire a horse-and-carriage as a date night option, but virtually no one uses a horse as a daily mode of transportation.
Now we see fully self-driving cars are soon to be available to consumers. Many of the functionality is already there in some newer cars. Teslas can drive themselves on the highway and park themselves, and should soon be able to drive in the city. Already one of these cars is affordable to someone in the middle-class without too much financial strain, and they’ll only get cheaper as they’re more efficient to produce and they become more available to buy used.
There will definitely be some people resistant to making the change. A lot of people enjoy driving, some would rather stay in control instead of putting their life in the hands of a computer, though the computer will be much safer. I’m sure a lot of people liked and had emotional connections with their horses too, but the car won out. Eventually the utility of self-driving will put human-driving out of style. It’s smarter, safer, and gives you back the time you’d usually dedicate to driving. Of course they’ll still be used for recreation and sport, a plaything for the rich, but virtually no one will use one as a daily mode of transportation.