Far too often players make two mistakes when pushing. First, they push to the backhand over and Over and OVER. Second, early in their stroke they aim their racket where they are pushing, usually to the backhand, in an apparent attempt to make it absolutely clear that once again that is where they are pushing. This is a great collaboration with your opponent, but not a good way to win.
First, let's review what makes a good long push. It normally should be quick, low, heavy, deep, and wide. (Exceptions: sometimes you no-spin push as a variation, so it doesn't always need to be heavy; and sometimes you push quick to the middle so the opponent has to decide whether to use forehand or backhand.)
But there is one other important element - last-second changes of direction. If you aim your racket to the opponent's wide backhand, he'll likely react to that and prepare for a deep push to the backhand. If, at the last second, you change and quick push to the wide forehand, you'll likely cause havoc for your opponent as he makes a last-second lunge for the ball. Ironically, this is especially effective against players with strong forehand loops, the very players you would normally not push to the forehand against, since they are often edging toward their backhand side, looking to forehand loop from that side.
At higher levels, players push short more often, especially when returning a serve. If your opponent serves short backspin, instead of just pushing it short, why not aim to his backhand, and then at the last second drop it short to the forehand? Again, this causes havoc, and in this case you aren't challenging your opponent's a forehand loop. Moving in to return a short ball to the forehand takes time, so why not try to trick your opponent into anticipating the ball coming to the backhand, and watch as at the last second he lunges in for the short ball to the forehand?
Moral: Don't just be pushy, be deceptively pushy!