Two persons pushing hands. Pulling and grabbing at each other, one trying to throw the other, the other struggling to keep his balance. Not exactly my idea of pushing hands, but still, this thing about balance kept me watching. Yes, there seems to be something in there about maintaining balance.
Then I think back about myself, losing balance sometimes when I practise my routines.
Taiji is practise slowly, because it is only by practising slowly can you pay full attention to all the details. And one of the details is balance. About sensing how you shift your weight, how to maintain balance at all times. With practice comes proficiency, and with proficiency comes confidence. And with confidence, you can relax. You won't be tensed up when facing an opponent, because you have confidence in what you can do, because you know you have put in a lot of effort into training.
With training, everything becomes second nature, including maintaining balance while moving. Knowing your own centre of gravity becomes second nature. Knowing how to keep that center of gravity stable becomes second nature. No matter how you or your opponent moves, you are able to maintain your balance. That is half the battle won.
And that is why I practise. And practise.