Moving back off the left foot,we push our right foot back into place from the LF. We then pull our weight onto that RF hence "push & Pull"

I don't agree. There is no pulling of any description in this movement.
Try this experiment. Stand holding a table and put you right foot about 15 inches behind you. Lift the left foot off the floor so it can't do anything. Now try to pull yourself backwards onto that right foot. Without snapping your achilles tendon.

Phil. Easy! just push yourself back before lifting the table and the left foot then pull yourself onto the foot. When do we only step back 15 inches . An experiment to be realistic has to match the task at hand. No offence ment Phil.

"Moving back off the left foot,we push our right foot back into place from the LF. We then pull our weight onto that RF hence "push & Pull""

No, you push from the departing foot and then allow your weight to coast to arrival, or if anything you slow your arrival by using the arriving leg to redirect your path towards a more upwards trajectory.

Constrast the situation in a jive chasse where you pull the body onto the arriving foot by a slight rising action of the arriving foot - if you try to push off the departing foot in jive, bad things happen.