How the idea that skirts were solely for women came about in the West is not really answerable. The tradition that men could show more of their legs than women seems to go back into the depths of antiquity, like the tradition that men had shorter hair than women, though the concept that men who were not priests, judges, or had similar formal requirements for gowns/robes only wore bifurcated garments seems to date to the end of the Middle Ages/beginning of the Early Modern Era. It's deeply ingrained into many western cultures that skirts are "for women", and until well into the twentieth century it was just as deeply ingrained that women wore only skirts.

I have an older answer to How did women get to wear the pants around here? that may help to illustrate just how strong that tradition was.