There is a misunderstanding of the Arabic word Qawwam. Many translate it as authority. Therefore, many assume Allah says that men have authority over their wives.
When we take a look closer at the real meaning of the word Qawwam, we see that it means expressing care, loyalty, and commitment over and over again over their women.
In some matters, Allah has give men advantage over women. But in some matters women have advantage over men!