When God created man and woman they were equal. He took Eve from Adam’s side and they were one flesh. Adam was created first.
Adam and Eve disobeyed God by eating of the fruit from the Tree of Knowledge of Good and Evil. This caused sin and death to corrupt their minds and bodies. It was Eve that took of the fruit first and brought it to Adam. God punished the woman by increasing her conception and her pain, and by putting her under obedience to her husband.
This was a punishment.