They did not break the taxi laws of every city they operated in. The taxi laws of many cities only required a "medallion" for taxi-style car services that allowed passengers to "hail" the car on the street.

So-called "black" cars where passengers arranged transportation in advance were governed differently, and required no licensing or a different and more permissive kind of licensing. Black car services were already widely available in many cities from lots of different companies, often independent owner/operators - it's just that no one had provided a service that worked across many different cities and was available conveniently as an app.

I won't claim that Uber and Lyft broke no laws, because there are a lot of jurisdictions in the world, and I don't know the laws of all of them, but many cities regular taxies and black cars very differently.

Edit: Why the downvotes? Am I wrong? Evidence would be appreciated.

When Uber started, they were all black cars anyways. It was a couple of years (iirc) until "normal" cars were allowed to drive for Uber.

As soon as the mobile phone was invented this system was obviously stupid, who invented it in the first place?

Those laws harmed consumers and would not be changed.

Lots of just causes broke unjust laws.

Uber drivers working 80 hours a week to survive because they have no workers rights like taxi drivers do would beg to differ.

Have you ever driven a taxi? Worker’s rights are a joke. Talk to your cabbie in New York about worker’s rights. The cabs are owned by large firms. Cabbies are hired and fired all the time for arbitrary reasons. And the wages are really low for the driver. But the owner makes a bunch as does the investor that owns the medallion license.