If the crafty males gave their seals to they women while they were away from the city, that's called delegation. They women were then free to go through all the crummy hassles that they still enjoy today. Women yack. The men got the heck out to have some peace and quiet. As today, women still control what 98% of the men want, and if there is any real power, it is there!
"On the other hand, the seals were the symbol of authority..."
on still another hand, maybe the seals were just status symbols, otherwise meaningless, like those rings used in the recent past to "raise" the heads of women -- whoever had the most rings won. Of course, it did kill them in time...