If you want to play table tennis at a high level, you really should learn to loop any deep backspin ball. There are, of course, exceptions, but they are few (such as choppers and some blockers). On the forehand side, where you have a big hitting zone, you should never really need to push against a long backspin. Think of this as a given – deep backspin to your forehand means you forehand loop. Don’t even think about it, just do it.
On the backhand side, ideally you should also loop any deep backspin. However, there are times where you might get caught too close to the table against a quick, aggressive push, and since the body is more in the way on the backhand than on the forehand, you might have to push. Also, you can get away with pushing on the backhand more because you have an angle into the opponent’s backhand, where most opponents aren’t as good attacking. Of course, some have great forehands from the backhand side, and others have great backhand loops, so it all depends on the opponent.
Learning to loop these deep backspin is a technique issue, and you should work with a coach or watch the top players to learn how to do this. However, here’s one important tip – if you want to be ready to loop against deep backspin, hold your racket relatively low. Many players hold their rackets too high and so are rushed trying to get them down to loop.
Since you are going to loop deep pushes every chance you can, should you learn to push against deep backspin? On the backhand side, yes, since most players do have to do this at least sometimes. On the forehand, probably not. You may learn to push with the forehand by pushing back and forth against deep balls, but that’s just to develop the shot. At the higher levels, the forehand push is done almost always against a short backspin only. Against deep backspin, many top players literally never forehand push, and if asked to do so (perhaps in a demonstration), some find the shot awkward to do since it’s not something they ever practice.