Why do progressive dances travel counter-clockwise around the floor and not clockwise?

Because we're in the northern hemisphere. In Australia they go around the other way of course. Dancing in central america and Africa understandably has some problems and so isn't as popular (besides, it's just too hot).

No seriously, two possible thoughts:

It's easier to go this way because the offset in the parntership makes right or natural turns somewhat easier, but they tend to be slightly underturned, and underturned naturals easily take you in a nice counterclockwise oval. Offset on that side goes back to various social customs, issues of which side you'd wear your sword on, whatever.

Other thought: well, which way do they go around in horse races? I don't know, but it might be similar

Sarcastic Smoothies suggestion makes sense but I think it probably goes back further than that. The waltz was a relatively late introduction to the ballroom, and was considered scandalous that a gentleman should hold a lady so closely in public!

Prior to this couples would have danced holding hands. The lady would have been on the man's right side to avoid his sword. The progressive part of the dance would have been a promenade or walk around the room where the man would have shown his beautiful lady to the onlookers. She would have been on the outside of the circle to graciously accept their applause, so the promenade would have been anticlockwise round the room.

Thanks for the replies to my query. Having read this before, I believe the theory of the lady being positioned on the gent's right side to avoid the sword scabbard is the most reasonable one. In the UK any male dancing Classical Sequence, positions his left hand on his left hip. This could depict the male holding the sword handle to avoid it being caught between the legs whilst dancing.

Actually, I learned recently that the sword theory is bunk. Men in that day would never wear a sword to a formal event such as a ball.

Athletes run counter-clockwise around the track, and i believe this started in ancient Greece