Savvy readers will notice that we've skipped 11:2–16. That's because they're some of the most obscure, difficult to translate and interpret passages in the Bible. The Lectionary likes to take shortcuts like that.
11:2–16 is definitely a case of not knowing when Paul is quoting the Corinthians and when he's giving his own opinion. I would argue that he's likely using the rhetorical device of an imaginary debate partner. I think the summation of Paul's point is verses 10 and 11: "A woman ought to have authority over her own head…woman is not independent of man or man independent of woman." In other words, the church is made up of mutuality and equity, not hierarchy.
I will point you to the best article I know of on this passage: https://www.linguistsoftware.com/Payne2006PP1Cor11_2-16.pdf