It's about control of fertility.
A woman always knows her baby is hers. The time and effort she puts into raising this baby is partially down to her surety in this matter.
A man cannot KNOW a baby is his. He can look for physical features. He can take his wife's word.
How much easier it is to believe a child is yours if you are safe in the knowledge that YOU are the only man to have clapped eyes on your wife's face for 20 years!
And hence the hijaab is born.
It never was to protect women. It was to control women's fertility, something men have long considered as something wrongfully given to women to control themselves.
Controlling a woman's fertility is the point of covering oneself in any way, indeed, is the point of marriage itself. All these silly little customs end, in so many words, with "Nobody's allowed to look at you as a sexual person and you're not allowed to fuck anyone else until I'm DEAD, get it?"