Liability - some states hold property owners liable for third party criminal acts if they ban firearms. While that is not a landlord tenant law, if you live in one of those states, and ban your tenants from possessing firearms, and a criminal breaks in and injures the tenant, there may be liability.
Source?
Don't have one, and now that I went to look at the state I was thinking of (off the top of my head) to post something in response, learned that I was wrong about what that state's law says, so . . .