"Did I get this right when you say. The step must leave before the beat and finish after the beat."
No, you got it wrong. What I said was:
"It a step is going to land "on" the beat, then it must start BEFORE the beat and end AFTER the beat."
Which if you would bother to pay attention to how a step is defined is so obviously true that there is really no point in your continue to argue with it.
"Have you heard the count one and, and, is where the step ends."
If you are dividing beats in half, and trying to match beats to steps at that crude level of precision, then the steps will begin on the half beats, which is to say each step will begin on an and.
So for example you would have one half beat of time between the and after three and the strike of beat one, which would constitute the first half of STEP one.
The placement of step one - which occurs when the step is about half done - would fall squarely on beat one. And then you would have a half beat of time between beat one and the and after one, which would constitute the second half of step one.
"The argument is too silly for words. Of course the foot leaves before the beat. The foot can't arrive if it doesn't leave can it."
Yes - and that period of travel from feet passing to step placement is defined to be part of the current step.
Yet if you want the foot to land on the beat, that period of travel that constitutes the first part of a step will have to occur during the "and" of the PREVIOUS beat.
Don't you see now, how the beats are offset from the steps?
"But don't drag beginners with you into what you think is arguably right."
All I am doing is expressing what would actually have to happen in order for your desire to land steps on the beats to be accomplished. Stated in the langauge of technique it doesn't look pretty, does it? Which is why I strongly recommend not worrying about this. Learn to create the rise and fall at the appropriate points in the action without regard to the music. Then learn to fit the whole thing to the music, not on the level of half beats, but rather on the order of entire measures.
"The instructions should be RF forward on the beat of one."
Absolutely incorrect. It is right foot LANDS on the beat one according to you - which obviously means that the right foot must start forward well before beat one - specifically during the second half of beat three.
"Or whatever it says in the technique book. Remembering Alex Moore does mention beats with steps."
Not in the way you keep imagining. He does not NAME the beats. Instead, he assigns a period of time measured in beats to each step - but in this case, the names for that period would be much closer to "and one" than to "one and". At least if you still are wanting your foot to land on the beat!