Re: Aikido and Tao Te Ching
"All beings support Yin and embrace Yang and the interplay between these two forces fill the Universe. Yet, only at the still, between breathing in and breathing out, can one capture these two in perfect harmony."
The first thing I would note is that translations of the Tao Te Ching can vary wildly. I would encourage you to look into a variety of interpretations to get more perspectives on what was originally written.
That said, the above quote is compelling on its own merits. Aikido is very much about finding a balance and right relation between Yin and Yang. As for the second part, all things that turn have a center of stillness. All things that move on a line have a source or origin of movement, and that is also a ground of stillness. All levers have a fulcrum. These are common, everyday mundane truths, and very much germane to an understanding of the mechanics of aikido.
You've asked a very penetrating question, and I will hazard an opinion that much mainstream aikido is not taught according to the above statement. By looking very deeply into your own question, I believe you can arrive at a better, fuller understanding of what aikido can be.
Finally, see also T.S. Eliot's "Four Quartets:"
"At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is"