Driverless cars are the future. That's almost indisputable. Not to say that drivable cars won't exist (likely with the ability for automatic control), because they almost certainly will, but the point is that a majority of car trips will be undertaken in a car that is largely driving itself.
There are really only two questions, which are: how far in the future and what will the ownership/rental/hire/pooling/sharing breakdown be.
I think 25 years is possibly a little too near for the level of disruption being predicted here.
That said, I think the scenario they are predicting is a sensible one and one not really addressed by several of the commenters, above.
That scenario is not that people won't own cars but that families that would otherwise own two cars (one for mum and one for dad) will, in a driverless future, own just one car and use some sort of sharing service to replace their second car.
There are already car sharing services available now - of all different types. There are services like GoGet where cars are purchased by a company that you rent them from. There are also services like CarNextDoor and DriveMyCar, that allow private owners to rent their car when they're not using it. Carpooling is also modernised with services like Carpool One, allowing you to search for an arrange car pooling.
While all that exists now, it becomes that much more convenient with driverless cars. With GoGet, you have to actually GO to get the car; with driverless cars, they will come to you, just like a taxi.
People will STILL own their own cars, of course but over all, it is likely that there will be less cars per person because most cars spend most of their time sitting around doing nothing.
Yes, there will be demand at peak times and if you drive to work, you will probably want your own car. But, if you are single or don't have kids then perhaps you will rent your car out on Saturday mornings* and a family with two kids that need to be at two different boring child sport venues at the same time might hire your car for one of the trips, using their own car for the other.
Again, this is perfectly possible and happens right now, but the necessity of actually going to get the car is a barrier now. If the car is there when you walk out your front door, that's a hell of a lot more convenient.