Doesn't matter how many times you say it: it's not "ride-sharing". Here's the way it works: someone picks you up from an address/street-side location they weren't specifically planning to go to, picks up a passenger they have not previously spoken to, takes that passenger to a specific destination that the driver was not specifically planning to go to, after which the passenger is charged and the driver repeats the process.
The thing with 'ride sharing' is that the goal for the driver is to actually get to some destination, at which time the driver will stop driving and get about whatever task was the main point in driving to that location in the first place.
I.e. it's carpooling.
If he driver is making the trip specifically for commercial purposes, rather than taking additional passengers in order to share the costs of a trip he/she would have to take anyway, that's a taxi service.
Nothing there represents any judgement on Uber as a company or a service. Whether you like it or hate it is irrelevant to what it is and what it isn't.