Sitting on Seed-Corn
The subsistence crop is the young and crunchy tips of a fast-growing coral; the juicy polyps are eaten along with the calcium carbonate they have built around themselves.
This particular polyp reproduces through budding. At the end of the growing season, those polyps that have not been harvested for food (by breaking off the coral tips, in bulk, forcefully, by then men) are carefully extracted from the remaining tubes. The small buds -- several per polyp -- are broken off and will be replanted next season. The oversized, juicy, un-shelled parent polyp is a special treat, enjoyed at the harvest festival.
Crucially, the polyp buds grow slowly. Very slowly. And unlike grain seeds, they need care. They must be kept in moving water so they get enough oxygen. But they must also be kept away from all the small pests that would love to get them while they are unprotected by their coral tubes. This is not "storing seed corn in a granary" as we know it -- it's closer to caring for a child.
As a society develops agriculture, it has two choices as to who the caretakers are for the unplanted polyps. It can be the men (defined here for convenience as the subset of the population with greater physical strength) or the women. Caring for the polyps takes time and effort and energy -- a huge amount of it -- but doesn't require strength. Those societies where the men are caretakers are missing out on using the men's labor on other, less important but more specialized, tasks. So those where the women are the caretakers -- watching over the seed polyps while they prepare food, make clothing, and do other dextrous but not strength-limited tasks -- are economically more productive over all. So these societies prosper.
But power over the seed corn is power over the tribe. The watchers don't just assure the food supply for the next year, they choose when it is planted, how much is held back for next season. They choose what portion of the crop must be used for seed rather than eating. And they prepare the ritually-important (and also just delicious) harvest festival meal, whose bounty declares that there will be food next year as well.
Rather than on land, where the power to supply food for future survival goes with men (hunting, etc), in this world it goes with the women.