Here is a question that has been ask to us, maybe the answer can help some of you....

Here is the explanation of your question about this verse from 1 Corinthians 11:10
1 Corinthians 11:10 (NKJV)
For this reason the woman ought to have a symbol of authority on her head, because of the angels.

This passage is actually the subject of various explanations sometimes.
I'm not saying mine is the best, because there are several versions. But it is in any case, what seems the most in agreement with the Bible.
I'll try to be as short as possible in this comment.

First of all, I totally agree with you in saying that the angels do not change, nor the word of God.

This passage can raise two main questions:
1. What is the sign and from which authority depends the woman?
2 What are doing here the angels in this passage?

The sign on the head of woman, of which Paul speaks about here, is a veil. So if things do not change as we have said, one could say that they should wear a veil even today.

In fact we must go a little further upstream. The veil here is only a consequence of having a sign of the authority which she depends, and nothing more.
If we take another translation (CEV) and so, because of this, and also because of the angels, a woman ought to wear something on her head, as a sign of her authority. (1Corinthians 11:10).

We can see here that the woman received an authority when she is born again (the same as man). This authority comes from Christ of course.
In other words, we could say that, woman must show the angels that she has an authority that was given to her, as well as the man, which comes from Christ. Or we can also say: woman must show to the angels the authority she has received, also coming from an authority above her: Christ.

This sign lies in the fact that women voluntarily agree to submit to the man. At that time this submission resulted visually, as a veil worn on the head. But Paul said a bit further that actually, this is not the veil that is most important, because it is a custom of that time.
But the woman being the equal of the man before Christ, her hair is considering as a veil. It is therefore on the attitude that women must concentrate and not on the form. As the form (the veil) will change depending on times and customs.

Today there is no more veil among women in most countries.
But at that time the veil was compulsory in this society that is why Paul said that women should respect the customs of this society.
Today Paul would say about the same subject: "woman must show the authority that has been given to her (as to the man) by not trying to supplant the man or manage him, but remain equal.
The veil is therefore only a form of the application, in the fact to show the authority given to the woman, by an authority, which is Christ.

Now why "because of the angels '?
The Bible shows us that angels are messengers, but they are also witnesses to what happens on Earth. (1 Tim 5:21).
The Bible also shows that there are assemblies in heaven, God with the angels. (Job 1:6, Job 2:1).
That was the woman who was drawn from man. She has been created for the man. She was also the one by whom sin entered first into a human being (Eve).
From these facts, and especially in the consideration of the women condition, at the time when this passage has been written, people might have thought that women would not be at the same spiritual level than man and that she could not have access the same things for instance.

But the woman has received exactly the same authority as the man who both have received it from the same authority, which is Christ. For this, the woman must show to the angels, who are witnesses of our lives that they have understood and accepted the authority that they have received also from Christ. This authority they received from Christ, put them at the same level as men, not lower, but not higher either. And it is by agreeing not to put herself higher than the man, that the woman shows the angels the sign of the authority upon which she depends: Christ.
This understanding on the part of the woman, may be seen only when the woman will not attempt to place herself above man. For example, and only for this time only, by veiling her head.

When the angels are in assemblies before God, they may bear witness about this condition of equality of the woman, by the authority that she agreed to receive.

Now why the angels need to be witnesses… Whereas God is omniscient?
Why is it that woman shows the angels that she understood her status?
I think that this is part of the things that we will know later...

Bye for now...