Man does not take his origin from woman, but woman takes hers from man.

For it was not man who was taken from woman, but woman who was taken from man.

For the man is not from the woman. He establishes by two arguments the pre-eminence, which he had assigned to men above women. The first is, that as the woman derives her origin from the man, she is therefore inferior in rank. The second is, that as the woman was created for the sake of the man, she is therefore subject to him, as the work ultimately produced is to its cause. [1] That the man is the beginning of the woman and the end for which she was made, is evident from the law. (Genesis 2:18.) It is not good for a man to be alone. Let us make for him, etc. Farther, God took one of Adam's ribs and formed Eve. (Genesis 2:21, 22.)

Footnotes

1 - "Ainsi que l'oeuure tendant a quelque fin est au dessous de sa cause et fin pour laquelle on le fait;" -- "As a work fitted for some design is inferior to its cause and the design for which it is made."

For the man is not of the woman - The man was not formed from the woman.
But the woman of the man - From his side; Genesis 2:18, Genesis 2:22-23.

For, the man is not of the woman - Bishop Pearce translates ου γαρ εστιν ανηρ εκ γυναικος, αλλα γυνη εξ ανδρος, thus: "For the man doth not Belong to the woman, but the woman to the man." And vindicates this sense of εκ, by its use in 1-Corinthians 12:15. If the foot shall say, ουκ ειμι εκ του σωματος, I am not of the body, i.e. I do not belong to the body. He observes that as the verb εστιν is in the present tense, and will not allow that we should understand this verse of something that is past, γαρ, for, in the following verse, which is unnoticed by our translators, will have its full propriety and meaning, because it introduces a reason why the woman belongs to the man and not the man to the woman. His meaning is, that the man does not belong to the woman, as if she was the principal; but the woman belongs to the man in that view.

(7) For the man is not of the woman; but the woman of the man.
(7) He proves the inequality of the woman by the fact that from the man is the substance of which woman was first made.

For the man is not of the woman,.... In the present state of things, and according to the ordinary course of generation and propagation of mankind, man is of the woman, though not without the means of man; he is conceived in her, bore by her, and born of her; but the apostle respects the original formation of man, as he was immediately made by God out of the dust of the earth, before the woman was in being, and so not of her:
but the woman of the man; she was made out of his rib, and took both her name and nature from him; God was the author, and man the matter of her being; her original under God, is owing to him; and therefore as he was first in being, he must be superior to her: this serves to prove all that has been as yet said; as that man is the head of the woman, the woman is the glory of man, what he may glory in as being from him; and therefore there should be this difference in their appearance at public worship.

is of . . . of--takes his being from ("out of") . . . from: referring to woman's original creation, "taken out of man" (compare Genesis 2:23). The woman was made by God mediately through the man, who was, as it were, a veil or medium placed between her and God, and therefore, should wear the veil or head-covering in public worship, in acknowledgement of this subordination to man in the order of creation. The man being made immediately by God as His glory, has no veil between himself and God [FABER STAPULENSIS in BENGEL].

The man is not - In the first production of nature.