1 Corinthians 11:3 (CWSB)
3 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.
.the head of the woman is the man ….
the word translated head here means in authority, and this relates to a marriage setting. 
It says nothing about the quality or inferiority of any of the two genders. Some read this to mean that the man is superior to the woman but God never said that , this scripture never said that , instead it says in effect that the man is the head over his wife.

In the book of John 5:16-18
16 And therefore did the Jews persecute Jesus, and sought to slay him, because he had done these things on the sabbath day.
17 But Jesus answered them, My Father worketh hitherto, and I work.18 Therefore — the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God.
The word translated EQUAL here is – ísos- in GRK meaning Equal, alike in quantity, quality, dignity (Strong’s dictionary )

We see that in 1 Corinthians 11:3 …..and the head of Christ is God.
We can see here that the scripture says that God is the head of Christ , signifying that He ( God the Father ) is in authority,over the Lord Jesus and from John 5 : 18 ….equal … both in quality and dignity.
We can therefore say from these spiritual facts that even though the woman is subject to the man (her husband) , she is not inferior to the man , we know that the woman may even be smarter or richer than her husband but the Bible commands that she should still be subject to her husband’s authority because of demons
Please note that , there is a statute of limitation to this authority which God gave to the man. This can be found in Deuteronomy 13:6-8 . A man is not allowed to lead his wife or family away from God and still be said to be in authority.