Paul was not a woman hater. He was a man who accepted God's truth.
1 Timothy 2:14-15
14 And it was not Adam who was deceived, but the woman being quite deceived, fell into transgression. 15 But women shall be preserved through the bearing of children if they continue in faith and love and sanctity with self-restraint. NAS
Isaiah 3:12
12 O My people! Their oppressors are children,
And women rule over them.
O My people! Those who guide you lead you astray,
And confuse the direction of your paths. NAS
Women have an essential and vital role in the home:
Proverbs 6:20-21
20 My son, observe the commandment of your father,
And do not forsake the teaching of your mother;
21 Bind them continually on your heart;
Tie them around your neck. NAS
Proverbs 10:1-2
10:1 The proverbs of Solomon.
A wise son makes a father glad,
But a foolish son is a grief to his mother.
2 Ill-gotten gains do not profit,
But righteousness delivers from death. NAS
However, Paul teaches the Biblical standard of the authority of the male in matters pertaining to faith and the life of the Body of Christ. As Christ (a male) is the Head of the Body so men are the head of the family and commissioned as sub-shepherds answerable to the Chief Shepherd.