Don

IMO, the FIRST thing to see about 1 Cor 11 is that the argument Paul is making does not make much sense to us today.  This means it is a “puzzling passage” and requires digging.  In other words, while doing 1st century context for a NT passage is ALWAYS a good thing, in this passage it will be required.

Another aspect is that 1 Cor would be read to the congregation by a literate person.  There were various factions in Corinth and each faction would be looking to see where Paul agreed with them or not.

Another point is that “every man” is describing a group, as such it MAY include females under the Greek masculine plural usage.  It is not clear when it is first mentioned whether it does or not.  In any case, how exactly is Christ the “head” of every human or perhaps male human?  As you point out, many people/males do not accept Christ as their authority.

Putting these last 2 ideas together one can see there would be some dramatic tension as the letter was being read.  Who is Paul agreeing with?

Another aspect is the article usage “ho aner” in 1 Cor 11:3.  The Greek article is used to make a noun definite, as in a specific person.  When a man has been identified previously, then it is that man.  In this case, I think it is “the man” is identified afterwards, in 1 Cor 11:8, namely Adam.

So there is a lot of ambiguity in 1 Cor 11:3 when considered by itself, but I think the pericope helps explain it.