This claim seems to be the root of every anti-AirBnB argument: AirBnB rentals eat into the resident housing supply.
But this is simply solved by zoning and regulation. In any given city there is some number of residents and some number of visitors, and some number of permanent and temporary beds for them to sleep in. Yes, AirBnB shifts some of the housing stock from resident to visitor - but, if that's what economic forces are commanding then the zoning & regulation should adapt, not fight it. It's not a capacity issue, just one of allocation.