The average car sits unused (parked) for well over half of its life (I'd say 90%, but I don't feel like research right now, and the concept holds at 50%). If we assume 100 1-hour rides are needed in a day, and each person uses their own vehicle, we need 100 cars, despite the fact that we need 100 car-hours. If we can optimize with a service like Uber, we would only need 5 cars to provide 100 car-hours in a day.
Obviously, trips are not completely fungible, but I think the central concept is clear above.
The second piece is that those 5 cars will be replaced much sooner than the 100 individual cars. That's where the utilization comes in. If everyone drives themselves, then the stock of cars must equal peak demand. If services like Uber combine riders (via UberPool - the typical car has more than 1 passenger seat that is unutilized in the typical commute) and provide utilization for cars at 50% of the day, then the total stock of vehicles would be lower than required for self-driving.
These two effects combine leading to fewer cars.