What it boils down to is this... Tom Peters is and always has been a passionate humanist. He believes in our human potential to build a more compassionate, just, and sustainable world.
If you look at this quote from a humanist perspective, then, I think Tom is saying that managing requires all that it is to be human.
Managing is the job for which we are perfectly evolved, and, thus, perfectly equipped.
To lead, inspire and grow a handful of other human beings will draw on all your best human qualities, starting with your capacity to care.
As your confidence grows and you become comfortable with the responsibility, you will find it tremendously fulfilling.