1 Corinthians 11:3

The third comparison he makes is of God to the Lord, when he says: The head of Christ is God. Here it should be noted that this name, “Christ,” signifies the person mentioned by reason of His human nature: and so this name, “God,” does not refer only to the person of the Father but the whole Trinity, from which as from the more perfect all goods in the humanity of Christ are derived and to which the humanity of Christ is subjected. It can be understood in another way, so that this name, “Christ,” stands for that person by reason of his divine nature; then this name, “God,” stands only for the person of the Father, Who is called the head of the Son not by reason of a greater perfection or by reason of any supposition, but only according to origin and conformity of nature; as it says in Ps 2 (v. 7): “The Lord said to me: you are my Son; today I have begotten you.”

http://dhspriory.org/thomas/english/SS1Cor.htm#111 

Referring to the use of “head” to describe the relationships between husband and wife and the Father and the Christ – “Thus one expression has different meanings, according to the difference of person and substantive relationship.”

- From his Commentary on Paul’s Epistles (81.120-21). 

But dost thou understand the term "head" differently in the case of the man and the woman, from what thou dost in the case of Christ? Therefore in the case of the Father and the Son, must we understand it differently also. "How understand it differently?" saith the objector. According to the occasion [136] . For had Paul meant to speak of rule and subjection, as thou sayest, he would not have brought forward the instance of a wife, but rather of a slave and a master. For what if the wife be under subjection to us? it is as a wife, as free, as equal in honor. And the Son also, though He did become obedient to the Father, it was as the Son of God, it was as God. For as the obedience of the Son to the Father is greater than we find in men towards the authors of their being, so also His liberty is greater. Since it will not of course be said that the circumstances of the Son's relation to the Father are greater and more intimate than among men, and of the Father's to the Son, less. For if we admire the Son that He was obedient so as to come even unto death, and the death of the cross, and reckon this the great wonder concerning Him; we ought to admire the Father also, that He begat such a son, not as a slave under command, but as free, yielding obedience and giving counsel. For the counsellor is no slave. But again, when thou hearest of a counsellor, do not understand it as though the Father were in need, but that the Son hath the same honor with Him that begat Him. Do not therefore strain the example of the man and the woman to all particulars…

 

To account for which; it was likely that this sin would have thrown our race into a state of warfare; (for her having been made out of him would not have contributed any thing to peace, when this had happened, nay, rather this very thing would have made the man even the harsher, that she made as she was out of him should not have spared even him who was a member of herself:) wherefore God, considering the malice of the Devil, raised up the bulwark of this word and what enmity was likely to arise from his evil device, He took away by means of this sentence and by the desire implanted in us: thus pulling down the partition-wall, i.e., the resentment caused by that sin of hers. But in God and in that undefiled Essence, one must not suppose any such thing.

 

Do not therefore apply the examples to all, since elsewhere also from this source many grievous errors will occur. For so in the beginning of this very Epistle, he said, (1 Corinthians 3:22, 23.) "All are yours, and ye are Christ's, and Christ is God's." What then? Are all in like manner ours, as "we are Christ's, and Christ is God's?" In no wise, but even to the very simple the difference is evident, although the same expression is used of God, and Christ, and us. And elsewhere also having called the husband "head of the wife," he added, (Ephesians 5:23.) "Even as Christ is Head and Saviour and Defender of the Church, so also ought the man to be of his own wife." Are we then to understand in like manner the saying in the text, both this, and all that after this is written to the Ephesians concerning this subject? Far from it. It is impossible. For although the same words are spoken of God and of men, they do not have the same force in respect to God and to men, but in one way those must be understood, and in another these. Not however on the other hand all things diversely: since contrariwise they will seem to have been introduced at random and in vain, we reaping no benefit from them. But as we must not receive all things alike, so neither must we absolutely reject all.

http://biblehub.com/commentaries/chrysostom/1_corinthians/11.htm 

He says that as Christ is subject to God as his head, so is the man subject to Christ, and the woman to the man. We shall afterwards see how he comes to infer from this, that women ought to have their heads covered. Let us, for the present, take notice of those four gradations which he points out. God, then, occupies the first place: Christ holds the second place. How so? Inasmuch as he has in our flesh made himself subject to the Father, for, apart from this, being of one essence with the Father, he is his equal. Let us, therefore, bear it in mind, that this is spoken of Christ as mediator. He is, I say, inferior to the Father, inasmuch as he assumed our nature, that he might be the first-born among many brethren. 

- From his commentary on I Corinthians

And the head of Christ is God; that is, the Father, not as to his divine nature, for in respect to that they are one: Christ, as God, is equal to his Father, and is possessed of the same divine perfections with him; nor is his Father the head of him, in that sense; but as to his human nature, which he formed, prepared, anointed, upheld, and glorified; and in which nature Christ exercised grace on him, he hoped in him, he believed and trusted in him, and loved him, and yielded obedience to him; he always did the things that pleased him in life; he prayed to him; he was obedient to him, even unto death, and committed his soul or spirit into his hands: and all this he did as to his superior, considered in the human nature, and also in his office capacity as Mediator, who as such was his servant; and whose service he diligently and faithfully performed, and had the character from him of a righteous one; so that God is the head of Christ, as he is man and Mediator, and as such only. 

http://biblehub.com/commentaries/gill/1_corinthians/11.htm 

The head of the man is Christ; the head of woman is the man; the head of Christ is God. If this concatenation be disturbed in any of its parts, ruin must be the result. The head is that on which the body is dependent, and to which it is subordinate. The obvious meaning of this passage is, that the woman is subordinate to the man, the man is subordinate to Christ and Christ is subordinate to God. It is further evident, that this subordination is very different in its nature in the several cases mentioned. The subordination of the woman to the man is something entirely different from that of the man to Christ; and that again is at an infinite degree more complete than the subordination of Christ to God. And still further, as the subordination of the woman to the man is perfectly consistent with their identity as to nature, so is the subordination of Christ to God consistent with his being of the same nature with the Father. There is nothing, therefore, in this passage, at all inconsistent with the true and proper divinity of our blessed Lord. For a brief statement of the scriptural doctrine of the relation of Christ to God, see the comments on 1 Corinthians 3:23. It need here be only further remarked, that the word Christ is the designation, not of the Logos or second person of the Trinity as such, nor of the human nature of Christ as such, but of the Theanthropos, the God-man. It is the incarnate Son of God, who, in the great work of redemption, is said to be subordinate to the Father, whose will he came into the world to do. When Christ is said to be the head of every man, the meaning is of every believer; because it is the relation of Christ to the church, and not to the human family, that it is characteristically expressed by this term. He is the head of that body which is the church, Colossians 1:18. Ephesians 1:22, Ephesians 1:23.

https://www.studylight.org/commentaries/hdg/1-corinthians-11.html#3