I take “praying and prophesying” in 1 Corinthians 11 to be a synecdoche for church worship. This best harmonizes with Paul’s comments regarding the place of women in worship elsewhere when he says that they are to be silent (1 Corinthians 14:34-35; 1 Timothy 2:11-12). I have spoken with my wife about these things. She now wears one during worship. Some sermons that deal with this subject well.
As for “because of the angels”—I think Fairbairn’s handling of this phrase is the most sound and sensible I have encountered. He reasons that it is an analogy: as man corresponds to God, woman corresponds to angels. Here are his full comments:
We see, then, the fitness and propriety of the veiled appearance of the woman’s head—it is the becoming sign of her place and calling, as made of man, and, in a sense also, for man. But why should this be said to be because, or for the sake of the angels? Whatever may be meant by the expression, one thing should be distinctly understood regarding it—that, from the brief and abrupt manner in which the allusion is made—not a word of explanation going before or coming after—it can have reference to no recondite or mysterious point—nothing in itself of doubtful speculation, or capable of being ascertained only by minute and laborious search. Points of such a nature, together with the Rabbinical or heathen lore, on which they are grounded, must be out of place here, as the allusion (had it referred to such) could only have tended to perplex or mislead.
Proceeding, therefore, on the ground now laid down, we have to dismiss from our minds all the peculiar and unusual applications of the term angels sometimes adduced by commentators; and also all fanciful notions regarding the acts of real angels such as their supposed habit of veiling their faces before God (which is never mentioned of angels, strictly so called), or having a sort of superintendence and oversight of Christian assemblies (a matter also nowhere else intimated in any earlier Scripture:) and we have simply to consider, whether there be any broad and palpable facts respecting the angelic world, which, without violence or constraint, may be fitly brought into juxtaposition with the proper place and bearing of women. We know nothing of this description, unless it be what their very name imports their position and calling as ministering spirits before God, from which one section of them, indeed, fell, but which the rest kept, to their honour and blessing.
This, however, is enough; it furnishes precisely the link of connexion between them and woman. Her place, in relation to man, is like that of the angels of God; it is to do the part of a ministering agent and loving help not independently to rule and scheme for herself. It is by abiding under law to man, that she becomes either a subject or an instrument of blessing. Hence, when she fell, it was by departing from this order, by attempting to act an independent part, as if no yoke of authority lay upon her, and she might be an authority and a law to herself quitting her appointed place of ministering, for the coveted place of independent action. So, too, was it, in the higher regions of existence, with the angels that lost their first estate; they strove, in like manner, against the prime law of their being, which was to minister and serve, and aspired to be and act as from themselves. By this vain and wicked attempt they fell; and the fall of Eve, through their instrumentality, was but the image and echo of their own. Now, is it unnatural to suppose that the apostle, while tracing up the matter concerning woman’s place and bearing in society to the origin and fountain of things, should also have reminded them of these instructive facts? should have pointed their thoughts to the higher region of spirits?
The order here—he virtually said to them—the order of things in this lower world, serves as an image of the heavenly. Relations of superiority and subservience exist there as well as here; and the harmony and blessedness of both worlds alike depend upon these relations being duly kept; to disregard them, is the sure road to confusion and every evil work. Let the woman, therefore, recognising this, and remembering how the evil that originated in ambitious striving in the heavenly places, renewed itself on earth by the like spirit taking possession of her bosom—feel that it is good for her to wear perpetually the badge of subjection to authority. It is at once safe and proper for her to retain it; and so, instead of constantly repeating the catastrophe of the fallen angels, she will show her readiness to fulfil that angel-relationship, with its ministrations of service, for which she was brought into being, and exhibit before the blessed ministers of light a reflection of their own happy order and loving obedience.
—taken from pp251-53 of Hermeneutical Manual, found here for free: https://archive.org/…/hermeneutical00…/page/252/mode/2up