San Francisco wants people who rent out their homes through Airbnb and other online platforms to follow some rules, and it wants the platforms to advertise only those rule-abiding listings — or face steep fines.

That means Airbnb and others must stick to advertising San Francisco hosts who have registered with the city and haven't exceeded the number of nights they're allowed to rent. The penalty? Platforms can be fined up to $1,000 a day per violation.

Now, Airbnb is suing its hometown, arguing that it's not responsible for making sure hosts follow city rules and that San Francisco, the place that birthed some of the world's most innovative startups, is undermining a bedrock principle that allowed those companies to flourish in the first place.

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