Drawing Circles When Pushing Hands

Last night when I was pushing hands with my teacher, we were practising how to just draw circles smoothly, in as light a manner as possible. My teacher was telling me that whenever I push hands, all I need is to relax and draw circles, and I will be able to neutralise all attacks, and if my opponent uses brute force or resists, he will lose his balance.

What my teacher did was that he drew big circles, leading my movements towards the extremities of my centre of gravity. When I push, he will use my strength to lead me further forward. When I retreat, he will follow my force and make me move back a little further. Then, just when you least expect it, he draws me just a little beyond the edge, and I would fall. All these, while simply drawing circles.