Some of these responses are absolutely laughable. Let me clear up some of the most egregious.

Swords? Folks, by the 1800's, swords were something officers used to keep the cowards from running when their flintlock pistol had already been fired, or to point where the men were to shoot, or to signal a maneuver or charge. Muskets and canons were the weapons of war. Frankly, from the reformation forward, no gentleman would go to a social occasion with a sword. Even the knife and trencher were pure middle ages.

When walking together, a man with his lady, the man walked on the right, the position of honor. In the military, this continues to this day, which is good, because if the lady walked on the right, she would get an elbow to the head everytime the guy saluted. Remember, in polite society, arranged marriage, and the "giving" of women to seal political deals, was common until well into the last century. It would have been very rare for a woman to have the position of honor, such as is the case with Queen Elizabeth and Prince Philip.

As to why the line of dance is counter-clockwise, I don't know, but it has nothing to do with swords. I would hazard the guess that it has mostly to do with right handed nature of the dance frame, the mechanics of the dance, and tradition.

One could as easily ask the question, why do clocks go clockwise, and what is clockwise if the clock is digital?