In 1 Corinthians 11 Paul writes, “But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God” (v. 3). In this verse, the word “head” refers to one who is in a position of authority over the other, as this Greek word (kephale) uniformly does whenever it is used in ancient literature to say that one person is “head of” another person or group. So Paul is here referring to a relationship of authority between God the Father and God the Son, and he is making a parallel between that relationship in the Trinity and the relationship between the husband and wife in marriage. This is an important parallel because it shows that there can be equality and differences between persons at the same time. […]
Just as the Father and Son are equal in deity and are equal in all their attributes, but different in role, so husband and wife are equal in personhood and value, but are different in the roles that God has given them. Just as God the Son is eternally subject to the authority of God the Father, so God has planned that wives would be subject to the authority of their own husbands. (Wayne Grudem, Biblical Foundations of Manhood and Womanhood, pp. 48-49)
1 Corinthians 11:3 is a/the linchpin passage in the Eternal Subordination of the Son (ESS)-meets-Complementarianism argument. Denny Burk, the current President of the Council on Biblical Manhood and Womanhood, has said as much himself (see, e.g., HERE). Three premises are required for the ESS/Complementarian argument to succeed.