But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God. Every man praying or prophesying, having his head covered, dishonors his head. (5) But every woman who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved.
1 Corinthians 11:3-5

Admittedly, this is a difficult passage. Those who do not believe the Bible is authoritative will usually dismiss this passage (from v.3-16), insisting that it is either wrong or culturally irrelevant. But for we who believe the Bible is inspired, inerrant, and therefore authoritative, we must wrestle with it. Here goes.

Scripture is clear that male and female roles exist, and that they are different, even though males and females are intrinsically equal.
Paul substantiates this by pointing to the Godhead (v.3) and to creation (v.9 & 14).
So far, none of this is cultural, but God ordained, and therefore cross-cultural and timeless.
The references to head-coverings is a different matter. A small number of Christians insist Paul’s reference to head coverings is likewise not cultural but God-ordained, and therefore women are to wear head coverings, at least in church.
A more widely accepted understanding, is that the issue of head coverings is a cultural example that made sense to the people to whom the letter was originally written. Because it isn’t culturally understandable in our culture, while the part about the God-ordained male and female roles is binding, but the example of head coverings is not. Head coverings are a cultural expression of a spiritual reality.

Are you still with me?

So then, how are we to put this into practice in our cultural setting?

Embrace the reality that male and female differences are God-ordained and binding.
Accept the ways in which our culture illustrates this correctly.
Reject all thought that God-ordained male and female distinctions and roles are irrelevant, and may be ignored or rejected.