1 Corinthians 11:3 is not about “headship.” It is about “unity” which is the meaning of the joint-body imagery used by Paul. Verses 4-6 are not Paul's opinions but are a proposal from the legalists at Corinth that he quotes. Then he refutes their ideas and restates his own in verses 7-15.
In 1 Corinthians 11:3 Paul reminds his Jewish readers, who are monotheists, of the importance of unity. Three times he points to independent elements that together make up one unit. The image he uses is that of the parts of the body that, united, make up one whole body:
He states his main idea in the first line of verse 3, and then adds two subordinate parallel images to illustrate it. In his reference to the parts that make up the body Paul challenges the reader to answer the question, Just who is “every man”?
“Every man” is every believer – every man and every woman who is a Christian. This image is parallel to the one Paul uses in Ephesians 5:23: “Christ is the head of the church.”
1 Corinthians 11:3: Christ is the head of every man
Ephesians 5:23b: Christ is the head of the church
An extraordinary response
Paul begins his response to those who did not hold to the tradition he had taught the Corinthians with some word play. Usually a “play on words” has an extra element in it that draws attention to the fact that something extraordinary is being said, even though ordinary words may be used.
In 1 Corinthians 11:3, Paul uses “every man” in Greek to stand for “every person – male or female.” Writing “every man” he makes a gentle play on words to make a point: Do some of you want to focus only on what a man is free to do in Christ? Not I. I will focus on every man in Christ because I want you to focus on what every person – male or female – is free to do in Christ!