"AirBnB" comes from "AirBed & Breakfast." The "air" part isn't related to, as you've suggested, something "not solid or fixed." It's a reference to an "airbed" a.k.a. an "air mattress." The idea was basically paying to rent an air mattress in someone's house.
Before AirBnB, "BnB" was a very uncommon way to abbreviate a "Bed & Breakfast". People generally used "B&B." But you can't used an ampersand in a domain name, hence, "bnb".
Again, I feel like you're proving my point here. AirBnB is a comfortable name now -- as-in after it became a multi-billion-dollar company. But that wasn't the case when the company launched. The name was strange.