Kephale

The literal meaning of the Hebrew word “kephele” is the head on ones shoulders. Metaphorically, it can be used in a variety of ways (to be determined contextually) or it can mean literally the head on one’s shoulders.

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Gordon Fee pg. 149, “Discovering Biblical Equality”.
Kephale in 1 Cor. 11:3, Paul metaphorical use of “head” in verse 3 ………………
1. This is both its first occurrence in Paul’s writings and its only appearance in a context where “the body” is not mentioned or assumed. Later when Paul speaks of Christ as “head” in relationship to the church (Eph. 4:15-16; Col 2:19) it is a metaphor not for “lordship” but for the supporting, life-giving role that in ancient Greek thought the (literal) heas was understood to have in relationship to the physical body.
2. ……….at issue, finally, in this whole passage is the nature of the relationship perceived between God and Christ.
3. What we know from the evidence is that when the Jewish community used this metaphor, as they did frequently in the OT, it most often referred to a leader or a clan chieftain. On the other hand, although something close to this sense can be found among Greeks, they had a broader range of uses, all of which can be shown to arise out of their anatomical understanding of the relationship of the head to the body (its most prominent or important part; the “source” of the body’s working systems, etc).
4. The earliest extant consistent interpretation of the metaphor in this passage is to be found in a younger contemporary of Chrysostom, Cyril of Alexandria (d.444?), who explicitly interprets in terms of the Greek metaphor: “Thus we can say that ‘the head of every man is Christ’, for he made by (dia) him…as God:’but the head of the woman is the man’, because she was taken out of his flesh…Likewise ‘the head of Christ is God, because he is of him 9ex autou) by nature” (Ad Arcadiam et Marinam 5.6). That is , as with Chrysostom’s understanding of the two pairs (God-Christ, Christ-man), Cyril is ready to go this way with all three pairs because of what is said in ver 8: that the woman was created from the man. Not only was the idea that the head is the source of supply and support for all the body’s systems a natural metaphor in the Greek world, but in this case it also supported Cyril’s Christological concern (not to have Christ “under” God in a hierarchy), just as it did for Chrysostom.
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To put an interpretation of “authority over” for the man toward the woman in 1 Cor. 11, is to do the same with God and Christ, which was a heretical understanding which Athanasia fought hard against.