Arabs spread it first, then various African tribes, and when Islam began spreading to the civilized peoples in the Levant and Iran, the religion was "softened" in many ways, and a philosophical and mystical element entered. When the Turks, a people similar to the Mongols and used to committing the same kinds of atrocities as Mongols were famous for, converted and took over the caliphate, they suppressed the relatively humanistic form of Islam that had developed in the Middle East
There's a book by the late Nabeel Qureshi, a Pakistani convert to Christianity, who wrote a book about women before Islam. Islam states it gave women rights; his book showed they enjoyed property rights independent of men and could divorce without the consent of a man. Islam appealed to clannish tribes who wanted power and women, so that explains why the Koran reads like a war orgy. The early conquest of Arabia was a bloody orgy of violence and the religion spread through the sword. Ironically, many of their pre-Islam pagan traditions remain, such as using crystals as charms or the evil
as Jews use the hamsa hand. One woman was even put to death for pointing this out, even though she was right and they were engaging in idolatry.
Turkey under the Sultans brought the end of the Byzantine Empire and it only had religious tolerance thanks to Suleiman the Magnificent, who prioritized secular law. Yes, he strangled his sons but his reforms gave him the name "law giver". The Ottomans' role in slavery is also overlooked and they are not forced to acknowledge it or pay reparations as whites are. Don't expect Hasan to grovel for the crimes of his ancestors.
But you are right: the religion didn't invent misogyny per se. It had to have already existed. Out of the religions of India, the Sikhs didn't think menstruation was a curse and that women on it weren't "unclean". In many households menstruating women aren't even allowed to touch food because they think they have rendered the food impure. A similar practice was done in Buddhist Tibet; it took a secular government to abolish it.
I've heard that Muslims like Dagestanis in Russia tend to be rather chill, because they allow their women to be educated and aren't stingy about head coverings. It's usually Afghans, Pakistanis and fresh converts who are the worst. Afghanistan was once a Buddhist country and is heavily inbred. Even if you eradicated Islam, those patriarchal norms would not disappear overnight. Men have to have the capacity to change. Jews, for example, will have a bunch of second wave feminists and will allow women to serve in the IDF, or keep them segregated from the wailing wall and on public transport. Ultra Orthodox Jews have a TFR of 6. Average ashkenazim? 1-2. They're the ones attacking Palestinians on settlements and will inherit the country . It ain't looking good.
India, though? It's the most overpopulated place on the planet. Their men have literal shrimp dicks, but that's never stopped them from breeding. I was just reading an article on historic marriage and menarche rates, and while it the average was 14 for first period and 18-20 for marriage, it was 12 in India. Even China forced girls to marry at 15. India also started chattel slavery via it's caste system but you don't see them groveling in apologies over it.
)