That doesn't explain why Uber is more about sharing than taxi companies, nor why Airbnb is more about sharing than the old way of renting your flat.
Sharing your car or home (whether the latter is rented or owned) is very easy without apps and people have been doing it for just about as long as cars and homes have existed. What the apps facilitate is making money from arms-length rentals to strangers. This may be a form of sharing, but even if so its a fairly specific one with its own name, its just that using an accurate and specific label rather than a misleadingly general one doesn't make as good marketing copy -- "sharing" sounds warm and friendly and positive, "rental" not so much.