Do I have to stop using Airbnb?

No, and most hosts should not. Keep your listings running and add a direct site beside them. The platforms are genuinely good at reaching people who have never heard of you; that is worth paying for. What you stop paying for is the introduction to someone you have already met.

The two work together through your calendar. Connect the iCal link from every platform you are on, and a booking taken anywhere closes those dates everywhere.

There is one rule worth taking seriously.

Do not divert a booking in progress. Messaging a guest through a platform to tell them to book on your site instead breaks the terms you agreed to when you listed. Platforms look for exactly this, and the penalty is losing the listing that is still bringing you new people.

What you can do is be findable. Your website address in the welcome book, on a card by the kettle, in the email you send after they check out. A guest who comes back on their own months later is not a diverted booking; they are a returning customer.

Some hosts eventually go direct-only. That is a decision to make after a couple of seasons, when you can see how much of your business is repeat and referral, not on day one.