Session.openActiveSession(this, true, new Session.StatusCallback() {
        @Override
        public void call(final Session session, SessionState state, Exception exception) {
            if (session.isOpened()) {
                Request.executeMeRequestAsync(session, new Request.GraphUserCallback() {
                    @Override
                    public void onCompleted(GraphUser user, Response response) {
                        if (user != null) {
                            Log.d("Access_token", session.getAccessToken());
                        }
                    }
                });
            } else {
                Log.d("SESSION NOT OPENED", "SESSION NOT OPENED");
            }
        }
    });
For Android 2.3.6 everything works as should, user gets prompt login dialog, enters data and app goes on. I thought that it was android versions fault but it turs out that the login isn't working when there is facebook application installed on the phone!