Why swirling water?

He says "to give it life!". I.e. Nick first explains that modern water is dirty and lifeless, so he filters it from nitrites, pesticides, chlorine etc. and then agitates water  'to give it life', and warms it up a bit to achieve proper dough temperature. 

I first thought he agitates water to get rid of chlorine smell, but he actually tries to oxygenate it, for the lack of better term, so it is as if it came from a brook, alive, bubbly, and agitated. 

My French is so old and rusty, that I cannot keep up, though I could listen to him for hours.

I had imagined that swirling would tend to oxygenate the water, but it's much more beautiful the way Nicolas (and you) express it.

Happy baking!

Cathy