Paul does talk about head-coverings for men and women. In the context of a few verses before Chapter 11 -- "Be without offense both to the Jews and to the Greeks and to the church of God," etc., Paul praises his addressees for remembering what he transmitted to them previously (11:2), and then he recapitulates what he transmitted to them (verses 3-9). But then he revises that, in light of what is true "in the Lord" (verse 11) and of the fact that "everything is from God" (verse 12, cf. also 10:31 "...you do everything to the glory of God"). And then comes the rest, with the gist that "the hair is given in place of a covering" to both men and women (verse 15; note that the KJV "her" in "is given her" is an addition, to be removed). In verse 16, I think what Paul is referring to when he says "we don't have such a custom," etc., is the liking to be contentious. This takes him to a discussion of "divisions" further on (verse 18 ff.).
In any case, if Paul never met Jesus, where does his authority come from to say
1 Corinthians 11:1 wrote:
Be ye followers of me, as I also am of Christ. 2 Now I praise you, brethren, that in all things you are mindful of me and keep my ordinances as I have delivered them to you.
Why should I keep Paul's ordinances?
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I just dropped in to see what condition my condition was in.
Strewth!