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.

Another way of looking at push pull is from the same foot. We swing the LF back by first pulling it with the ball of the (RF) and then pushing it with the heal of (RF). NOTE: I still have to read the previous replys Thanks Dave.

No,you push from the departing foot and then allow your weight to coast to arrival? To arrive on the ball of foot which then has to pull the weight onto the foot.
Using the arriving leg to redirect your path ? Yes by pushing of the heal of that foot.
You slow your arrival? Yes you slow your arrival by the speed at which you pass over the whole foot"ball & heal"

If we agree you slow your arrival and re-direct it, why do you persist in this idea of pulling on the arriving foot? Pulling makes you go faster after all. And you are already going plenty fast enough if you use the departing leg properly.

When we place our weight on and over the ball of the back foot we then have to pull it onto the heal,but also for the same reason that Geoffrey Hearn says we pull our weight over and through the front foot. I you can't agree that Geoffry Hearn is right on the forward step then you won't agree that it happens on the backword step. Soum, I am not disagreing with you,just stating another point of view. I don,t have the knowledge to give correct answers.

"When we place our weight on and over the ball of the back foot we then have to pull it onto the heal"

Only if you insist on outstepping your body flight. Since this forces you to break contact with your partner or arch you back to make room for the moving leg, there's two very good reasons (efficiency and appearance) to keep your leg swing in natural proportion to your body flight, such that arrival over the foot is automatic with no additional work required.

In practice, dances who have to pull themselves onto their feet cannot be considered to have body flight at all. They tend to be those who let the body fully or nearly stop over each step, reach the foot out, and then labouriously transfer from foot to foot. That's closer to tango, NOT waltz, foxtrot, quickstep or viennese.