Before answering that question, it will be helpful to see what the Greek word translated “head” meant in ancient Greek literature other than the Bible. The word is κεφαλή, and it is found in the following passages:
Greek: “Ζεὺς κεφαλή, Ζεὺς μέσσα, Διὸς δ᾽ ἒκ πάντα τελεῖται ῾τέτυκται” (Aristotle, On the Cosmos, LCL 401a).
English Translation: “Zeus is the head, Zeus the centre, from Zeus comes all that is.”
Greek: “Τεάρου ποταμοῦ κεφαλαὶ ὕδωρ ἄριστόν τε καὶ κάλλιστον παρέχονται πάντων ποταμῶν” (Herodotus, The Histories, 4.91).
English Translation: “From the headwaters of the river Tearus flows the best and finest water of all.”
In both of these passages, κεφαλή is used to represent “source.”
We find the same usage in the New Testament, concerning Jesus:
Greek: “καὶ οὐ κρατῶν τὴν Κεφαλήν, ἐξ οὗ πᾶν τὸ σῶμα διὰ τῶν ἁφῶν καὶ συνδέσμων ἐπιχορηγούμενον καὶ συνβιβαζόμενον αὔξει τὴν αὔξησιν τοῦ Θεοῦ” (Colossians 2:19).
English Translation: “They have lost connection with the head, from whom the whole body, supported and held together by its ligaments and sinews, grows as God causes it to grow.”
Greek: “ἀληθεύοντες δὲ ἐν ἀγάπῃ αὐξήσωμεν εἰς αὐτὸν τὰ πάντα, ὅς ἐστιν ἡ κεφαλή, Χριστός, ἐξ οὗ πᾶν τὸ σῶμα συναρμολογούμενον καὶ συνβιβαζόμενον διὰ πάσης ἁφῆς τῆς ἐπιχορηγίας κατ’ ἐνέργειαν ἐν μέτρῳ ἑνὸς ἑκάστου μέρους τὴν αὔξησιν τοῦ σώματος ποιεῖται εἰς οἰκοδομὴν ἑαυτοῦ ἐν ἀγάπῃ” (Ephesians 4:15-16).
English Translation: “Instead, speaking the truth in love, we will grow to become in every respect the mature body of him who is the head, that is, Christ. From him the whole body, joined and held together by every supporting ligament, grows and builds itself up in love, as each part does its work.”
In both Ephesians and Colossians, κεφαλή (head) is used to describe Jesus as the “source” of growth in his body, the church.
The same word, κεφαλή (head), is used in the New Testament to refer to the first man, Adam, as the “source” of the first women, Eve:
Θέλω δὲ ὑμᾶς εἰδέναι ὅτι παντὸς ἀνδρὸς ἡ κεφαλὴ ὁ Χριστός ἐστιν, κεφαλὴ δὲ γυναικὸς ὁ ἀνήρ, κεφαλὴ δὲ τοῦ Χριστοῦ ὁ Θεός (1 Corinthians 11:3).
“But I want you to realize that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God.”
The human race was created through Christ (John 1:3); he is the “source” of “every man.” Adam, the first man, was the “source” of Eve, the first woman (Genesis 2:22). God was the miraculous source of Jesus’ incarnation as a human being (Luke 1:35).
Some complementarians insist that 1 Corinthians 11:3 speaks of God as the “authority over” Christ, Christ as the “authority over” man, and man as the “authority over” woman. The context of the passage, however, does not support this meaning. In 1 Corinthians 11:11, Paul reminds the Corinthian church that just as a man was the source of the first woman, so too is a woman the source of every man. Rather than supporting the notion that “source” should translate into some kind of hierarchical rank, Paul reminds this church that women and men share being a “source” of life equally: “Yet, as believers in the Lord, women couldn’t exist without men, and men couldn’t exist without women” (1 Cor. 11:11). Paul is talking about “source” in the immediate context of this passage, not authority.
Despite all of these New Testament uses of κεφαλή to mean “source,” some complementarians will insist that “head” means “authority.” Sometimes they will cite the following passages:
And he is the head (κεφαλή) of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. (Colossians 1:18)
…having raised Him out from the dead, and having set Him at His right hand in the heavenly realms, above every principality and authority and power and dominion, and every name being named, not only in this age, but also in the one coming. And He put all things under His feet and gave Him to be head (κεφαλή) over all things to the church, which is His body, the fullness of the One filling all in all. (Ephesians 1:19-23)
Surely these passages tell us that Christ is the “head” in terms of having authority over the church, don’t they?
No, this is not Paul’s meaning.
The Risen Savior is presented here as having authority over demonic principalities and powers: “For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places” (Ephesians 6:12).
Jesus is seated far above these principalities and powers, and we–his body, which is connected to the head–are seated there with him: “And God raised us up with Christ and seated us with him in the heavenly realms in Christ Jesus” (Ephesians 2:6).
Jesus has authority over these demonic powers, and so does the church, in our union with Christ. How did Jesus accomplish this for us? By taking upon himself the form of a servant and dying on the cross: “And having disarmed the powers and authorities, he made a public spectacle of them, triumphing over them by the cross” (Colossians 2:15).
Jesus died and rose again, so that we might share his victory over sin, Satan and the grave. This is what Paul means when he refers to Jesus as the “head of the body” and “the beginning and the firstborn from among the dead” (Colossians 1:18). Once again, he is the “source” of our new life, and of our freedom from the power of a defeated foe.
What does “κεφαλή (head)” mean in the New Testament? Regarding Jesus and Adam, it means “source.” Adam was the “source” of Eve, who was taken from his side; and Jesus is the “source” of life, growth and freedom in the church. Referring to husbands as the “head” of their wives (Ephesians 5:23), Paul tells them, “love your wives, just as Christ loved the church and gave himself up for her” (Ephesians 5:25).
Is this language teaching male authority? On the contrary, let’s look at the example set for us by Jesus himself:
Jesus called them together and said, “You know that the rulers of the Gentiles lord it over them, and their high officials exercise authority over them. Not so with you. Instead, whoever wants to become great among you must be your servant, and whoever wants to be first must be your slave— just as the Son of Man did not come to be served, but to serve, and to give his life as a ransom for many.” (Matthew 20:25-28)
This example of NOT exercising authority over others is what husbands are commanded to imitate in the New Testament: “Husbands, love your wives, just as Christ loved the church and gave himself up for her” (Ephesians 5:25). Suggesting that this passage means that husbands should “rule over” their wives is the exact opposite of what Jesus taught and modeled for us through his life (and death) of sacrificial service.
When Jesus took upon himself the form of a servant, and was obedient to the point of death, he became the “source” of our life and freedom. This is what “headship” means in the Bible, and this is the example we are commanded to follow:
In your relationships with one another, have the same mindset as Christ Jesus:
Who, being in very nature God,
did not consider equality with God something to be used to his own advantage;
rather, he made himself nothing
by taking the very nature of a servant,
being made in human likeness.
And being found in appearance as a man,
he humbled himself
by becoming obedient to death—
even death on a cross! (Philippians 2:5-8)