"Today ,not yesterday. The right area of the chest touches that of the other. Right side to right side. If the ladies left side is strongly forward it will open the ladies right side and will result in a left side to right side and not right side to right side."

That's why the lady's left side is not only strongly forward, but ALSO filled out and back.

Words that seem to contradict, but don't actually...

This is how it was explained to me. If we stand square to each other with a measure on each shoulder neither one side or the other has any difference in width.
If the lady turns even slightly to her left that will decrease the distance between the
man's and her own shoulders on the man' s right side. This will now open the ladies right side. Now the biggest side is on the man' s left and ladies right.
To be correct today the big side is on the man' s right and the smaller side on his left. Which gives us a right side to right side contact
The right area of the chest of each partner touches that of the other and stays there. Look and you will be rewarded.

"This is how it was explained to me. If we stand square to each other with a measure on each shoulder neither one side or the other has any difference in width."

A property of both rectangles AND PARALLELOGRAMS.

"If the lady turns even slightly to her left that will decrease the distance between the
man's and her own shoulders on the man' s right side."

No, because the man has an equal and opposite trend to HIS left. Men are dominant in the standard hold, yes, but they are not inflexible rectangular monoliths.

Sorry to be a bit blunt, but to say that the lady's left side will be strongly forward, but also quite back, doesn't just sound contradictory - it is contradictory. I think maybe you had the correct picture in your mind, but need different words to describe it.
This is a topic which is of significant interest to me as i believe it is a weakness in our dancing, so i'm trying to follow this discussion.
What about "keeping the centres towards each other"? which has been impressed on me.
The text books all say the lady should not arch her back, but almost every single photo of champion dancers shows the lady doing precisely this.
Doesn't the lady need to be shaped to her left and also back? Stretching both sides of her torso? I mean in closed hold of course.
An easy fault appears to be for the lady to shape left, but also rotate upper body to her left, taking her centre away from her partner. It's easy for the man (who is shaping to some extent to his left) to do the same.
Maybe this "centre to partner" requirement causes the torsion required as it requires the lady to rotate to her right slightly(around the axis of her spine), while keeping her general shaping (i.e. the line of her spine)to the left. If the man does the same, the shoulder line will stay parallel, but the 'picture' is much bigger
i'm not sure of all this (otherwise i'd be a better dancer!!). It's very difficult to desribe here - much easier for a good coach to explain and demonstrate.

"The text books all say the lady should not arch her back, but almost every single photo of champion dancers shows the lady doing precisely this."

A lady's back will naturally be somewhat more curved than a man's, but what you see often goes mistakenly far beyond that.

If the lady is really getting her backwards poise right, the "arch" will move up to her upper back (where it takes the form of shoulders down and back) and down to her hip and knee JOINTS. Note that I don't mean the angle of the pelvis, which must stay aligned (in the context of a lady's anatomy) to her trunk, but instead an angle formed by the femur in the pelvis.
That's quite dramatically demonstrated in a throwaway oversway - at first glance there's a huge arch in the lady's back, but in fact most of it is her trunk vs. her thigh.

Arched Back. Firstly in Latin an arch in the back for either the man or the lady is out. In a competitions sway back will make you an also ran.
In Modern to deliberately arch the back will thrust the hips forward. This is OK in a Throwaway Oversway but not anywhere else.This applies to all dancing. Could you imagine a Ballarina with an arched back, or the male up there on the stage with an arch in the spine.
Slavik on his Latin DVD does give some advice on creating a straight spine.
Once upon a time in Standard the lady in her setup was taught to place the right bust on the man' s shirt buttons. Then to take it off clockwise a few degrees. The man also turned clockwise a few degrees. The right bust is not touching, it is off the man. Not anymore . The right bust touches the man's right and stays there. Quote. The right area of the chest of each partner touches the other. Go to the videos on this site and see for yourself.
One more thing. If the alignament of the spine is deliberately altered, the point of balance is no longer where it should be. Dancing of any kind is all about being balanced.

"In Modern to deliberately arch the back will thrust the hips forward. This is OK in a Throwaway Oversway but not anywhere else."

On the contrary, it is as wrong there as anywhere else! The shape of an oversway is a curve approximated by a series of straight lines between flexible points of the body, particularly the leg joints - NOT from the small of the back. In a well done throwaway, the pelvis will remain aligned to the trunk, just as in any other well danced figure.

"This applies to all dancing. Could you imagine a Ballarina with an arched back, or the male up there on the stage with an arch in the spine."

Sure... its wrong but you see it all the time, though the costumes are designed to hide it - meaning you see it more if you get to see people in street clothes.

"Once upon a time in Standard the lady in her setup was taught to place the right bust on the man' s shirt buttons. Then to take it off clockwise a few degrees."

You mistake is in thinking that the there was a clockwise rotation intended to take her off the man. There NEVER WAS. Instead, then, as now, there was a strong forward presentation of the left side. You might think of it as rotation, though that would be mangling the issue. But to say it was inteded to take her off the man is just grossly incompetent!

"One more thing. If the alignament of the spine is deliberately altered, the point of balance is no longer where it should be. Dancing of any kind is all about being balanced."

But where should that point of balance (well, center of mass, given that you won't always have your center of mass balanced) be?

Answer: to sustain movement, it will often have to be projected out into empty space, outside the footprint of the only standing foot. Off balance in plain english. If you try to resist this, you will destroy the alignment and fluidity of your dancing... YOU SIMPLE CANNOT CHANGE THE LAWS OF PHYSICS - denial won't help you one bit.

By all means pay a TON of attention to EXACTLY where you weight is. But don't kid yourself you can keep it literally balanced, because YOU CANNOT.

There are several shots of a Throwaway Oversway on the UK site.. The arch in the back can be seen and is for, apart from the visuale. simply to keep a balanced point between the couple. The balanced point is still there. It is as we are all aware a stationary pose.
From the book again. Page 12. Normal poise or position.
Care should be taken by the lady not to lean backward too much, or an ugly arching of the back will result.
It goes on. The backward inclining of the lady must be taken from the man. The position in no way assists the balance, but certainly makes the couple look attractive. By that I would say he is saying don' t overdo it.

"There are several shots of a Throwaway Oversway on the UK site.. The arch in the back can be seen"

I believe I have been pointing out that arching the back, despite being a MISTAKE is very COMMON at all levels of dancing. We are only human.

The second issue is that competition costumes are designed to lie about your shape, and where your waist is. Figuring out where the curve really is requires being able to imagine the body under the clothes, when the clothes have specifically been designed to hide that.

The net result is that a lot of what is actually shape in the leg and hip sockets will be mistaken by the unsophisicated observer as arch in the back. Add to that the arch that actually is in the back (but shouldn't be there) and you have what you thought you saw.

i think this comes into it. If we do an Oversway. We have a curve from our toe to our head. That we call a curve. If the same amount of curve is used back we call it an arched back. The reason it is neccessary to arch the back for both the man and the lady is because the left leg is taken behind by the lady and there is no change in the conection between the bodies. The right side to right side is still there.