1 Corinthians 11:3

But I would have you know According to St Paul's invariable rule, the question is argued and settled upon the first principles of the Christian Revelation. In the sight of God all men are equal; yet without distinctions of rank and office society could not exist. But equality and order are reconciled by the revelation of God in Christ.

the head "In the idea of this word dominionis especially expressed. As in the human organisation the exercise of dominion over all the members proceeds from the head; so in the family, from man; in the Church, from Christ; in the universe, from God." Olshausen.

of every man is Christ See Ephesians 1:22; Ephesians 4:15; Colossians 1:18; Colossians 2:19. As the head directs the body, so ought every member of Christ's Body to be governed and directed by Christ.

the head of the woman is the man Cf. Ephesians 5:23. "It appears that the Christian women at Corinth claimed for themselves equality with the male sex, to which the doctrine of Christian freedom and the removal of the distinction of sex in Christ (Galatians 3:28) gave occasion. Christianity had indisputably done much for the emancipation of women, who in the East and among the Ionic Greeks (it was otherwise among the Dorians and the Romans) were in a position of unworthy dependence. But this was done in a quiet, not an over-hasty manner. In Corinth, on the contrary, they had apparently taken up the matter in a fashion somewhat too animated. The women overstepped due bounds by coming forward to pray and prophesy in the assemblies with uncovered head." De Wette. Such persons are here reminded that according to God's word (Genesis 3:16; 1 Timothy 2:11; 1 Timothy 2:13) woman was designed to be in subjection, both in society and in the family. Of this last, woman's chief sphere, man was, by God's ordinance, the head. Yet (see below, 1 Corinthians 11:5) she is on an equality with man in her individualrelation to Christ.

the head of Christ is God Cf. ch. 1 Corinthians 3:23; 1 Corinthians 8:6; 1 Corinthians 15:28, and notes. Also St John 14:28. Possibly this may be added to prevent the idea from gaining currency that the interval between man and woman was in any degree comparable to that between Christ and man. And it also implies that the whole universe is one vast system of orderly gradation, from God its Creator downwards.