It happens, sometimes decisions are found in favour of the opposite side, same way you feel you are right so does the other person and in majority of cases, there can be only one winner which in this case, appears not to be you.
I would suggest you review Airbnb’s decision, put aside for a second what you wanted the outcome to be and take an objective view, does Airbnb have a point in its decision? It's hard to comment more specifically without any details but ultimately after thinking carefully if you still feel they are wrong in their decision and you have hard evidence to support your reasoning, then there is nothing to prevent you from writing a formal complaint letter regardless of the fact that they do or do not have an appeal process; concrete evidence that contradicts any actions Airbnb take/ their decision will always precede and demand a review of the situation as part of the investigation process of the complaint. Do bear in mind that if you follow this route it can be more time consuming, even stressful and does not gurantee the outcome you want as Airbnb may equally have evidence against you; weigh the benefits of accepting their decision against pursuing.
All the best,
Ama