From facing couples:

   The dancer on the right (usually the lady) steps forward to
meet the opposite dancer with a right forearm grip and
begins a full turn to return to her original position.

The dancer on the left (usually a man) will follow his partner after
she passes, taking the hand of the other lady as she
catches up and leading her to her home.

If the left hand dancer waits until the center pivot has turned
half before he moves ("Grab that guy and drag him home")
the result may be to pull the arm of the active lady backward
which is uncomfortable and much less smooth.

To see Flutter Wheel from more positions, click here: