From facing couples:

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

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

If the right hand dancer waits until the center pivot has turned
half before she moves ("Grab that gal and drag her home")
the result may be to pull the arm of the active man backward
which is uncomfortable and much less smooth.