While in theory you can start moving in either direction, leader forwards tends to be a bit more secure for the first actual dance step. As a result, if one wants to start a foxtrot with a feather finish, it can be better to precede this with a small forward hovering step to connect, and then move backwards into the feather finish.
Another thing to think about - we don't want to start a swing dance at the bottom of the swing, since that's the point where we should have maximum body speed. So we usually start with a prep step that is something of a downswing action during which we can build up a more normal amount of body speed than we would have from a cold start. In the hover and back into feather finish, we're pushing up the opposite side of the valley a bit, then swinging down through with body speed and up into the feather to start really dancing together.