Actually, Jesus probably DID cover his head every time he prayed. He was a Jew, after all, and Jews do not pray uncovered.
Now I find that very plausible as Paul was Jewish.
I actually prefer to look at commentaries on the topic, and especially ones that can decipher the Greek.
Bible hub commentaries is a favorite of mine:
1 Corinthians 11:4 Commentaries: Every man who has something on his head while praying or prophesying disgraces his head.
κατὰ κεφ. ἔχων] sc[1759] τί. See Fritzsche, Conject. I. p. 36. Buttmann, neut. Gr. p. 127 [E. T. 146].
Having (something) down from the head, i.e. with a head-covering. The Jewish men prayed with the head covered, nay, even with a veil (Tallith) before the face. See Lightfoot, Horae, p. 210 f. Michaelis, Anm. p. 244 f. Hellenic usage again required that the head should be bare on sacred occasions (Grotius on
1 Corinthians 11:2; Hermann, gottesd. Alterth. § 36. 18 f.), while the Romans veiled themselves at sacrifices (Serv. a[1760] Aen. iii. 407; Dougt. Anal. II. p. 116). The Hellenic usage had naturally become the prevalent one in the Hellenic churches, and had also commended itself to the discriminating eye of the apostle of the Gentiles as so entirely in accordance with the divinely appointed position of the man (
1 Corinthians 11:3), that for the man to cover his head seemed to him to cast dishonour on that position.................
22. 1 Corinthians 11:1-16 - Its Issues and Implications
WHAT KIND OF HEAD COVERING IS REQUIRED BY PAUL?
The Greek expressions used of the woman’s head covering seem to indicate that something more than a piece of cloth (or a hat) resting on the head is required. Not only should something be on the head, but something should hang down from the head to cover the hair:
… what Paul had in mind is a veil which covers the whole head and in particular conceals all the hair; something worn on top of the head like a present-day cap or hat does not really come within the scope of his argument.
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… it is probable that Paul is speaking of wearing a head covering of some kind, such as a shawl. That a shawl rather than a full veil is in Paul’s mind is indicated by the word
covering (
peribolaios) in 11:15, which is not the usual word for veil but probably refers to a wrap-around. The evidence in favor of this position is as follows: (1) The verb translated as “cover” in the
NIV (
katakalypto) occurs three times in verses 6-7, and related cognate words occur in verses 5 and 13. These words most often refer to a covering of some kind. For example, the angels who saw the glory of Yahweh in the temple
covered their faces (Isaiah 6:2). Judah thought Tamar, his daughter-in-law, was a harlot because she
covered her face (Genesis 38:15). Since the word almost universally means “to cover” or “to hide,” the text is probably referring to a hair covering of some kind. … Esther 6:12 (LXX) employs the same expression found in verse four,
kata kephales, of Haman, who hurried home mourning, covering his head in shame. He probably used part of his garment to do this. … To sum up: the custom recommended here is a head covering of some kind, probably a shawl.
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The Error of the Long-haired Jesus
Such a command had been in effect since the time of Moses. Whereas the King James Version translates Leviticus 10:6 as
“uncover not your heads,” the Jewish authorities always knew that this should be rendered
“Let the hair of your heads not grow long” (see Rashi on Leviticus 10:6; and it is so translated in The
Jerusalem Bible, Koren ed.).
This command of God was given again in the time of Ezekiel.
“They shall not shave their heads [that is, to be bald]
, or let their locks grow LONG they shall only trim the hair of their heads” (Ezekiel 44:20 RSV).