Explanation:

Back in the day a tradition of women stealing men’s hats and then demanding money to return it could be found all over Denmark.

It started when a woman had given birth and people came to see the newborn. Men had to hand over their hats when entertaining a house, and women started demanding money to give it back. Eventually men couldn’t walk past a field where a lot of women were working without being chased down and having their hats stolen.

The whole things was seen a pretty harmless though because the women didn’t demand a lot of money and didn’t harm the men, and sure, being seen without a hat was embarrassing for a man, but not like “Oh no my head is naked! My honor has been destroyed!” embarrassing, so no one pressed charges and it was allowed to continue for generations.
(And people probably thought the sight of a man running at full speed with a group of women at his heels grabbing at his hat was pretty amusing)

In some areas men started saying “No! I will not pay! Keep the hat!” and as a result women in those areas started wearing men’s hats as part of their casual clothes.