Driving a car is a complex and potentially dangerous activity, hence the license. A license to rent a place to sleep makes no sense.
Edit: Instead of responding to every single sub comment I will just add that car accidents kill 30,000 people a year. Whether or not you think AirBnB should be regulated, the analogy pairing their activity to the commonly fatal activity of driving is unambiguously on a different level. A more appropriate analogy is perhaps a fishing license.