Uber says there is a surplus, people driving cars with empty seats, and they attempt to capture that surplus. From an economic point-of-view that is a good argument. The surplus undeniably exists, and it would be beneficial to reduce it.
The argument on the other side is that this is an issue of public policy. Various countries have decided it is beneficial to legislate people driving strangers in exchange for money. The general arguments are ones of safety, but quality of service also comes into it. Again this is a reasonable argument. There is an information asymmetry when hiring a taxi (I don't know what kind of driver I'm going to get) so legislation reduces that.
The main point seems to be who gets to decide public policy? Uber and "Silicon Valley" types believe that private individuals and companies should be allowed to set public policy. Most others reject this.
The next argument is whether current legislation is appropriate and whether Uber has sufficient features to make existing legislation unnecessary. E.g. are ratings and ubiquitous GPS sufficient to reduce information asymmetry. If Uber wants to engage in this argument it should use the usual methods of setting public policy. I don't know if Uber has started any court cases but I expect they will be involved in some soon if not already, and this is one way to effect public policy.