We should note that the community of Corinthians were former pagans and not Jews.
The following is an explanation of the meaning of the passage in the context of the Corinthians, was provided under an answer to the related question Translation of 1 Corinthians 11:4:
The Greek text is κατὰ κεφαλῆς ἔχων - kata kephalēs echōn. The literal meaning is something like "having down of head". This sounds somewhat non-sensical, but the phrase is apparently a well-known idiom meaning to have one's head covered (see, e.g, Louw-Nida Greek-English Lexicon of the New Testament based on Semantic Domains).
Paul seems to have been alluding to a custom among pagan Greeks to put on some sort of head covering when prophesying.1 According to one Greek explanation from the 4th century, Paul was admonishing Christians who prophesied from imitating pagan customs while doing so:
Having anything on his head: He signifies that even though he pray with a bare head, yet if he has long hair, he is like one covered. For the hair is given for a covering.2
The idea is that it is superfluous to put on any kind of "headgear". This is reinforced a few verses later (v.7):
For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.
1. John Chrysostom, Homily XXVI on First Corinthians (tr.
from the Greek)