try logging out using this snippet
private void logout(){
// clear any user information
mApp.clearUserPrefs();
// find the active session which can only be facebook in my app
Session session = Session.getActiveSession();
// run the closeAndClearTokenInformation which does the following
// DOCS : Closes the local in-memory Session object and clears any persistent
// cache related to the Session.
session.closeAndClearTokenInformation();
// return the user to the login screen
startActivity(new Intent(getApplicationContext(), LoginActivity.class));
// make sure the user can not access the page after he/she is logged out
// clear the activity stack
finish();
}