“Push hands” in Tai Chi serves the same purpose as sparring in other martial arts; it’s a chance for you to apply what you’re learning on your own, in your own solitary body, in practice with other people. But push hands isn’t about speed or force or even about winning. In fact, if any of those three approaches are your first response to your partner’s actions in push hands, your partner will tie you in a knot before you can think.
Most teachers would probably say the first principle of Tai Chi push hands is to root, to feel yourself connecting into and through the ground. That makes it more difficult for the other person to get you off balance.
But my first principle has to be softness. If I’m tight and hard, I’ll forget all about my root, and everything else. So in push hands, as well as the rest of life, I’m starting to make “soften” my first thought, my first action, and my first reaction, in every circumstance. When you soften, you remember what you need, and you remember what you have (which of course is all you need).