Angry Birds POP requires permission to access your friends list on Facebook to display friends in the game. If this permission is missing, your friends will not be displayed. 

You can allow the game to display friends by navigating in your Facebook account settings

1. Apps
2. Angry Birds Pop
3. Remove the game from your account

Once this is done, open the game and connect back to Facebook. The game will request permissions again, so make sure to allow the game access to the friends list.

For more information on inviting friends to the game, please refer to the article here.