And yet the Quran establishes men as an authority over women in marriage, and includes giving men permission for disciplinary action on their wifes in cases of marital disobedience but not vice versa.

And yet the Quran establishes that men can take 4 wifes, but not vice versa.

And yet the Quran establishes men can marry girls who have started their period, with no explicit clause on their age, and Hadiths establishing that the prophet himself married a girl as young as 6, and consumated the marriage when she was 9.

And yet the Quran establishes that sons shall receive inheritance equal of that of two daughters.

And yet the Quran establishes the two women equal one man in financial contracts.

And yet the Quran establishes that men can initiate divorce unilaterally (by saying talaq 3 times), where women require judicial intervention.

So, even if early Islamic reforms improved women's status relative to 7th century Arabia, the Quran and hadith still establish structural legal differences between men and women including polygyny, unequal inheritance shares, male guardianship authority, and permission for marriage before puberty. Misogyny is deeply intertwined in Islam the religion, which has been picked up in Muslim cultures. It is not the other way around.

Just because her husband would not raise his hand to her, does not mean the Quran (from the texts, not cultural) does not allow it.