There isn't really an answer to this question. To quote from an earlier answer of mine:

The basic answer is: we don't know.

It's easy to point to this or that era as having fashionable male hairstyles we'd now consider "long" or cultural moments where women could crop their heads (which are what's given the most attention in the FAQ), but the fact is that we can find artwork showing adult men generally having shorter hair than women stretching back in the west and ancient near east for thousands of years. For instance:

• Woman wearing a cylinder seal, playing a flute (with long hair, put up), Sumerian, ca. 2600–2500 BCE vs. Seated male with cup and palm frond (and very short hair), Sumeria, ca. 2600–2350 BCE

• Group statue of a man and woman, Egypt, ca. 1850–1640 BCE

• Statue of Kedamun and His Family, Egypt, ca. 1550–1295 BCE

• Yuny and his wife, Renenutet, Egypt, ca. 1294–1279 BCE

• Amphora with twisted handles, Attic Greece, ca. 470 BCE (if you zoom in, you can see that the young man has a short ponytail while the woman has a substantial bun)

• Marble stele for a man, Attic Greece, ca. 375–350 BCE (three men with shorter hair; woman in the upper right with hair that is up and styled)

We simply don't have the textual sources that would let us know where exactly this trend comes from. Did it rise independently in multiple ancient cultures? Did it have one origin and spread from there? Did it originate in prehistory? At this time, it seems impossible to say.