Is it possible that Paul sets up a metaphor in v 3 that is to be carried
forward into the following verses? Thus, Paul expects the reader to see v 4
as, "Every man...having his head (Christ) covered (under authority)..." In
this fashion, Paul could be using the Corinthians' preoccupation with the
form of obedience (wearing of a hat) to illustrate the superiority of the
substance of obedience (the subjection of man to Christ, and woman to man).
In this manner, he shows the error of arguing over form when substance is
what really matters. In other words, I don't think Paul (nor God) cared
(cares) whether a man or woman had (has) long hair or short.
Roger Hutchinson