I was researching misogynystic verses in Quran and literally it says nothing about covering a woman's head. It has a saying about covering breasts but with a very long list of exceptions, where it can remain uncovered. So what went wrong?

Allah didnt use the word headcover? It says bikhumurihinna [24:31] or short khumur, which simply means cover. 

24:31 :

"And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their covers over their chests and not expose their adornment [i.e., beauty] except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess [i.e., slaves], or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed.