-a man who wants to know if she's late -a man who wants to be out hunting bison when she's likely to be grouchy -a man who wants to be home from hunting when she's likely to be doubled over with cramps -a man who wants to know when the moon will light up the night -a man who wants to know when the night will be especially dark

Probably someone with imagination might be able to come up with a longer list of why a man would want to know a 28-day cycle....

Once you start counting time in lunar months it's an obvious move to divide the month in two halves, and then to do that again, and divide it into four.

I wonder how old the concept of a week actually is.

Not that you are necessarily wrong but... A hunter who wants to go out at night and needs to know when it will be light/dark. Ditto someone planning/expecting an attack on/by a neighbouring tribe.

Or really anyone with some free time and interest (not uncommon)...

> What man would need to track the 28-days cycle of the moon?!?

A hunter of any gender who wants to know approximately when the animals migrate or give birth, would benefit.

Things that are easy enough for anyone to track and count:

day/night cycles

lunar cycles

annual summer /winter cycles

"four moons after the middle of winter" is therefor useful as it's possible to count, more easily so than "112 days after midwinter"

> What man would need to track the 28-days cycle of the moon?!? [..]

I'm a man and I actually track the moon cycles. I go skiing in the mountains during winter. If it's a full moon, or nearly so, I can plan on starting in the evening. With snow it's easy to ski in moonlight. If it's the wrong phase I can't plan on starting in the evening (typically Friday, for a weekend trip), I have to wait until the next day. There are other activities here which requires moonlight as well. It's important. Where it's snow, moonlight makes all the difference. I always kept track of the moon, especially when I was in my late teens and went somewhere hiking or skiing every weekend.

I can easily imagine how super important moonlight would be for neolithic people, for all kind of activities, hunting and more.

> The first astronomers and calendarians were women

You state it as if it were a fact.

Prior to the invention of fabricated light sources, the lunar cycle would be of interest to any humans that liked being able to see and walk at night.

Someone who hunts at night. My grandpa could always tell which lunar phase will we are at, despite never having periods.