Of course people can rent their property without Airbnb, it’s been done forever. The question is, what kind of rental business do you have. What Airbnb created was a platform to easily bring together people with space in their home and people who needed a place to stay short term. No need to make a website, advertise, draw up contracts, etc. Just snap a few pics, write some text and add your banking info. Boom, you’re “in business.” If, like me, you are renting out a room in a home there is no viable competitor. If you have a guest house, a basement apartment, the top floor of your home, the other side of a duplex, Airbnb is really the way to go. If you have an entire stand alone vacation rental home then VRBO is a viable competitor. You can make your own website and do your own promotion. In some markets booking dot com seems to be a strong competitor. But for most hosts without Airbnb they have no business. And people like to complain about them but the reality is they created the business, they own the platform, they have first mover advantage and at this time they are dominant in the space (and they want to dominate other spaces).
This is just anecdotal evidence but here is one guys story of being thrown off Airbnb and the effect it had. I’ve linked the concluding post but you might want to read the whole thing. After being off Airbnb the poster says "*But without them. We struggled so much. They represent 7 bookings for everyone we get else where. We even joke. If a Airbnb client wants to punch a hole in the wall. Give them a hammer."