Equanimity is not distance
Pema Chödrön makes the distinction cleanly: equanimity is not detachment. Detachment is another form of control — you manage your distance from things so they can't touch you. Upekkha, the Pali term, is more like a vast, steady ground that doesn't contract when something lands on it. She says the Bodhisattva ideal is radical openness — not less feeling but feeling without the defensive architecture around it.
I think this is what the tai chi teacher means by sung. And I think it's what Pharinee meant all along. The same instruction.
I just needed it from three directions.