Why Facebook AND Duolingo sign up?
How come you also need to set a Duolingo username and password when sign up with Facebook? Seems unnecessary. Why do Duolingo do this?
Have you thought about it the other way around? You can sign up for a Duolingo account and the Facebook implementation is an extra service for people who have FB (and are interested in getting Duolingo info on their pages). Duolingo offers its own independent experience for which it needs to have a way to keep track of its members.