Hi, I know how to resolve this issue!
Call airbnb and verify yourself, they will ask about 10 questions!
Then explain this issue and ask them to help you reset your account password. They will ask for the new email address to send the temporary password to.
Once you receive that temporary password, login using the old email id and the temporary password!
Then go to account settings and click on change password.
Enter the temporary password under the "current password" and enter and confirm the new password.
Once that is done, you can scroll down, click on edit email address. Enter the new one and it will ask you to enter the password for your airbnb account, you enter the password you just set, and its done!