It depends upon how you created your account.
If you originally created the account on facebook as a browser app, you are actually a facebook customer, not a direct BBE customer. Thus, you need to log into the app using facebook.
If that is not an option (I am not sure whether or not that ability exists), then you need to decouple your account from facebook in order to use the app. That makes you a direct BBE player... and you will not be able to log in using Facebook at this point, as your account is no longer associated with them.
In order to unbind your account from a social network you will need to do the following:
Please go to:
settings -> account
Select the option "Unbind account".
Fill in the requested fields.
You should now receive an email with a confirmation link. Click on the link to finish the process.
Use the email address and password to log in to the app.
I have retired from the game, but not from life.
In love with my Baby.