Was St. Paul a misogynist?

No, never; there was not an ounce of misogyny in him. What Paul wanted was for women to be cared for, protected, and loved, which is why he told husbands to love their wives, protect them, and care for them as the more fragile members of humanity; treat her like a queen and she will treat you like a king. You will not get that wholesomeness in the family if the wife is a tyrant, or wants to be the man, or wants to make all the decisions or make the money. That is also why the wife is meant to stay home with the children, because if you let her out of the house there are men waiting to seduce her and then treat her miserably; that is the way life is. So Paul was simply trying to protect women: here is your place, stay here in this cursed world where you can be protected and raise your children the way God wants. That is all he wanted. But a woman who does not want what Paul wants will call him a misogynist for it.