Uber is a far more modern way to get around. Uber also creates jobs for people who can't necessarily get a job as a cab driver, also uber fares are up to the driver so uber really supports the younger working class person wanting to make a good living or just some extra money.
Because they often have a much larger fleet than Uber, taxis employ more people than uber does, and inviting uber into a city will put a hole in the taxi industry, a hole Uber cannot fill. As well, uber is a large company and for cities outside of the United States, Uber does not pay all of its corporate taxes to the local governments, but taxis are often owned by local, small businesses, who pay all their taxes to the local governments, who use it to improve infrastructure and build things like schools and hospitals. So it is no wonder that Uber is illegal in more cities than it is legal.