Italy's law is quite specific on the matter, to offer transportation as a business you're either a taxi or a rent-with-driver (Noleggio Con Conduncente or NCC in Italian).

Taxi have their own finite licensing problem but NCC are easier to get. You still need a permit from the local Comune[0] and to abide to the rules. In exchange NCC vehicles can use the same fast lanes taxi can use.

The most contested rule is that NCC are hired only for specific rides (eg form A to B, or for N hours) and they need to go back to the garage between rides. They specifically requires the vehicle to be parked in the garage before accepting a ride, and the garage to be in the same Comune that gave the NCC permission.

This clearly doesn't work well for Uber as it doesn't have any garage, nor it's willing to accept the suboptimal usage the go-back-to-garage is going to cause.

Disclaimer: INAL, but I've talked to some Italian lawyers about this.

[0] https://en.wikipedia.org/wiki/Comune

edit: formatting