On the forehand side, when someone pushes long, it's almost always a good idea to loop. Because of this, many players are not comfortable forehand pushing except against a short ball. Against a deep ball, they almost always loop, and that's usually a good thing. The problem is when they play a chopper, where suddenly having a good forehand push against a deep ball becomes important.
When playing a chopper, one of the worst things you can do is attack over and over without letup. A chopper wins points on your mistakes, and so he wants you to play too aggressive, thereby making too many mistakes. Instead, it's almost always best to attack one ball, and if the chopper makes a good return against a strong loop - i.e. returns it so you can't put the ball away with relative ease - then you should usually push and start over. When they chop your loop back, you are usually getting much more spin than normal (especially if you loop to long pips), plus it's trickier to read accurately, plus the defender is already standing back there, in position for your attack. So instead of going for another risky attack, just push, bringing the chopper in, and then you can attack again. (This is especially true if they make a good chop return of your spinnier loops. If you loop with only a little topspin - i.e. roll the ball - then you generally get less backspin on the return, and so may be able to keep attacking until you see one to go after. It's a chopped return of your stronger, spinnier loops that you should more often push unless the ball is high.)
The problem is that, if you don't have a good forehand push, you'll make lots of mistakes. Matches are often won and lost on this simple shot, since so many attackers aren't comfortable forehand pushing against a deep backspin, and so lose far too many points that way. Or, since they aren't comfortable forehand pushing, they attack against balls where it would be higher percentage to push.
You could cover the whole table against a chopper with your backhand push, and many do - but that would mean you have to decide early on whether to forehand attack or backhand push, and so you might make the wrong call. It also means you would be telegraphing early on that you are going to push, and so the chopper can move in toward the table.
Instead, learn to forehand push against deep chops. That way, you can wait much longer before you decide whether to attack or push, thereby giving yourself more time to make the judgment, and not letting the chopper know early on which you will do. (In fact, it's often best to cover the entire table with your forehand loop and push against a chopper.) You might also find this valuable against other defensive players, such as a blocker who waits for you to attack - this allows you to push several balls before find the right one to attack. Or you can use it against an aggressive player who doesn't have a strong attack against push.
So even if you don't normally forehand push against deep balls, make sure to practice pushing with someone, including that not-as-often-used forehand push! The next time you play a chopper, you'll thank me for it.