The Exception is throwed as follows:
Work flow of Xamarin.Auth is as follows (I debugged inside the Xamarin.Auth source code):
1 -> You create an instance of Oauth2Authenticator, that will create an activty with a Webview inside. The Webview will open the Facebook login page.
2 -> You type login information and press Login.
3 -> You manually handle Completed event which fired by Xamarin.Auth if the login information was correct.
4 -> Xamarin.Auth finishs the activity.
5 -> Xamarin.Auth make a request to redirect_uri which was passed to Oauth2Authenticator.
As everyone can see, the step 4 & 5 is crazy. The author of Xamarin.Auth should fix this problem.