This stereotype may not be followed in the 21st century but we still see a majority of women having long hair while a majority of men having short hair and I know this was very much prominent in the 20th century.
My answer might not be much help but I do know that two trendsetters in the ancient world were Alexander and Scipio Africanus. Both of them came from societies where beards were expected to be worn by all men, and by shaving they popularized the new look
We have a good FAQ section on this topic to start your search with.
This question comes up pretty frequently, and has its own section on the FAQ. I apologize in advance for none of the answers being really definitive, but it's simply not really answerable for a few reasons.
One is that length is relative, and so some can argue that men having short(er hair than women) was a norm throughout the last X centuries while others say that no, short is more than just "not as long as possible" and the norm is more recent. You're not going to find a time with no differentiation between male and female hairstyles butting up against a time with obviously short male hair and be able to point to it and say that that's it.
Another issue is that it's underpinned by the idea of progress happening because of a single person/event/style becoming dominant and then naturally spreading, with no steps back along the way. This just isn't the way the world works. It's not the case that one culture adopted this norm and was then followed gradually by the rest. We can talk about where the current standards of male hairstyles come from in more recent history, but drawing a straight line back to antiquity would be a mistake, imo.