My main example of this are Athena and Artemis. They were both independent women without a husband and were responsible for male dominated domains, hunting and warfare. Athena is often depicted with spear, helmet and shield, which a respectable greek woman would never wear. This also applies to other cultures like Egypt or the Germanic/Nordic cultures. In my understanding the mythological world did not reflect the real life society, wich makes no sense.

Sorry if there is some strange grammar, my english is a bit rusty.