Hitting straight backhands, on both sides of the pony, are the worst mistakes made by beginners. During a polo game they are universally regarded as bad shots. In the majority of situations they give the ball to an opponent, and they cannot be received as pass by a team member.
Also, straight backhands will, too often, hit a pony or player, thereby ruining the flow of the game and possibly causing injury. However, although they occur seldom, there are two exceptional circumstances when a straight backhand could be required:

1. When the goal you are attacking is close, directly behind you and not defended.
2. When all the other players are blocking every available angle on both sides of you and the only open ground is directely behind you.

Nevertheless, I firmly believe that to practise them will cultivate a bad habit and it is therefore not justified, and they are not included in circles explanation.