Is there a historical reason as to why traditionally men bow and women curtsy?

A Lady's curtsey is a relic of those barbarous days when woman was expected to bend the knee on being ushered into the presence of men of rank and power, as an acknowledgment of her inferiority. Says John Aubrey, writing in 1678, "Till this time, the Court itself was unmannered and unpolished. King James's Court was so far from being civil to woman, that the ladies, nay, the Queen herself, could hardly pass by the King's apartment without receiving some affront."

http://www.sacred-texts.com/etc/mco/ml06.htm

Very interesting, thanks. But it should also be noted that in the presence of a King, in the court of King James, a man would have had to bow.

A man would also bow upon being presented to a woman; she in turn, curtsy. I'm sure the same happens now. It would take a very harden republican to not, without even meaning to, bow upon being introduced to the Queen. It would be an almost natural reflex. The woman stands in front of you: I doubt you'd give her a high-five.

No, my question is why that particular physical action: why the lowering of the neck for men and the bending of the knee for woman. How did this come to be?

I suspect it has to do with the dress. Even with just a short bow...a woman's dress would hit the floor. Thus, it seems a natural movement to pick up the dress as one performs any of the curtseys. I would think the fancy footwork of a curtsey evolved from that point.


https://en.wikipedia.org/wiki/Curtsey

Not the answer but interesting
The Catholic church's social customs and gestures often have a long history, in many cases extending back into the Middle Ages. Protestants, on the other hand, mostly originated in the late 16th century and after, when customs were undergoing substantial change. Kneeling, for instance, was not always a gesture of worship; in the Middle Ages and Renaissance it was often merely a gesture of honor or respect, like bowing or curtseying. Children routinely knelt when asking their parents for permissions or blessings -- even when wishing them good night! Commoners knelt to their overlords, and of course everyone knelt before the King or Queen. But the late 16th and 17th centuries saw a gradual substitution of a mere bow or curtsey for kneeling, and kneeling was increasingly reserved in Protestant circles for God alone.
http://paternosters.blogspot.com/2007/04/protestants-ii-worship-honor-and-virgin.html

Interesting...but, also NOT the answer. The question that is being asked was clarified in billythebrit's follow-up post:

"No, my question is why that particular physical action: why the lowering of the neck for men and the bending of the knee for woman. How did this come to be?"

In other words...Why does the woman curtsey and not bow and why does the man bow and not curtsey?

Bowing is a sign of submission - one is presenting one's neck to a person who probably has a sword. One is demonstrating that the other is superior and has the right ro chop, but also demonstrating that one has the confidence that the chop will not happen. Similar positioning responses occur in quite a few animals. A lady would not be in the position of acknowledging the other person as a military superior or conqueror, but the bending of the knee indicates a lowering of height, and thus an acknowledgement of the other persons superiority. Bows in males between equals or near equals are short and not deep like bows to a superior - just a quick bend of the neck and then straighten. This is continued in the nod to an acquaintance. It's all not so much a historical reason as a formalising of the responses common to us and animals.