Earlier quoted context omitted.
The argument that counters this is that hailed rides will be cheaper than driving what you already have. You don't need to make a new purchase to switch. Even if you have a recent model sitting in the driveway, you may choose to save money by hailing a car rather than driving your own. I don't know if it'll play out like that, but the article is pretty convincing.
Why would a car owned by someone else be cheaper than the same car owned by you? The obvious answer - dividing the cost of the car over more miles - doesn't seem right to me. Driving more miles doesn't generally increase the useful mileage lifespan of cars, it just wears them out more quickly.
The per-mile cost also includes the capital outlay for the car itself. In other words, it might not make sense for you to pay $40,000 for a new electric car, but it could make sense for three people to split that, and drive each persons per-mile cost down.
All of this is in reference to how fast the switch over could happen, and is why it might be much faster than any of us anticipate.