RE: Yes
So, women today MUST cover their heads as well?
The context is about men "praying or prophesying" (v. 4) or women "praying or prophesying" (v. 5). With the prophesying aspect, I'm assuming that the praying is public praying (or leading in prayer as we say today). So this head covering instruction isn't for all men and women just attending church. This is for the people doing some aspect of leading in the church.
And for background on the culture: Greeks were big on presenting who they are by what they say more than how they dressed. Romans changed that by being more about how one dressed. This is the Greco-Roman culture in the Corinthian church that Paul was writing to. Also related is that it was the custom for many religions in the area, including Judaism, for men to have their heads covered during religious ceremonies. That Christian men have their head uncovered is quite remarkable in my opinion.
Altogether, I take Paul's teaching here to be about two points to those leading some kind of teachings or worship or whatever in church: men should dress like we have a direct connection to Christ by having our heads uncovered, showing that Christianity is about a very real relationship to Jesus and not some standoff-ish relationship like is expected with other religions. And women aren't supposed to show off their hair like a harlot in that day (IMHO look like a Greek temple prostitute). Just like shaving the head is a disgrace (verse 5), perhaps as many Aphrodite temple prostitutes in Corinth were slaves (head shaven) forced into temple prostitution. Showing off the hair suggesting looking like a temple prostitute who was doing it willingly.
Again, the context in this is about women not having a hedonistic appearance when teaching (prophesying) or praying like the worldly people were promoting a woman's appearance (much like is done today). And men who are teaching/praying should promote an appearance that says us Christian men are different from other men in that we know we have a direct connection to our Lord. Now with the customs today being different, I wouldn't say women who lead in church should cover their hair. But the overall attitude of modest appearance should be adhered to. As should men promote an overall attitude of us having direct access to Jesus.
That’s how I see what Paul says there. I am not going to argue about it with you or anyone else. A question was asked and I answered it. If you don’t like the answer, live with it. So many people these days put their lives at risk just because they don’t like someone’s point of view. Very foolish, especially in person. I am old and literally don’t care any more. That guy the other day on video saying it would be the last mistake anyone ever made to stop a transgender from going into a women’s bathroom is one of the most inflammatory things I have ever heard one of those kind of people say. Why he hasn’t been arrested blows my mind.