@Stephanie2575 Do you have a contract with the letting agent? If so then it presumably details what happens when the relationship comes to an end. If not then I hope the one with the new letting agent does. Anyway if the original letting agent is in breach of its agreement then, if they will not see reason, your only recourse is to take legal action against them.
In this situation Airbnb is in a difficult position because, for all they know, you may be trying to steal someone else's account. Alternatively you may be trying to transfer the account from someone else to you which is against its rules. Quite how Airbnb sorts this out is beyond me I am afraid.