I have been meaning to write about this particular part.Languages generally develop many words to describe something similar that mean something to the person. Once upon a time 'man' and 'woman' seemed adequate, but those no longer work in many cultures.
Having discussed this multiple times over the years with many different people, I think “man” and “woman” is most workable in the context of the partner dance. The rest of the labels either fall short by creating wrong notion of what the role implies or in trying to be politically correct introduce labels that are one dimensional (only emphasize one attribute of the role).
Keep it simple. There is a man’s role and a woman’s role in partner dancing. That’s how the partner dancing evolved. Too bad that it offends “politically correct” sensibilities of many (mainly in the western world). There is nothing stopping a woman from doing man’s role.
This reminds me of a story that many might have heard. A rich man goes to an island and sees a young man resting/lazying under a tree. The story is a short conversation/dialogue between the two. To paraphrase the rich man asks the young guy what he is doing and then explains the virtue of working hard, how working hard begets money, yada yada. The young man asks “so?”. The rich visitor replies “so with money you earn, you get to enjoy life”. The young man retorts - “so what do you think am I doing now”. An unnecessary round about way to get to same results.