The fedora headship of Christ is an interpretation of 1 Corinthians 11:3-16 in which Paul tells the church in Corinth that men should pray with their heads uncovered and women with their heads covered.
There have been several interpretations of this passage, from women should wear veils to men should have short hair to married women should wear wedding rings when praying in church. The
fedora headship says that because Christ is the head of man and Christ wears a fedora, men are "covered" by Christ's fedora. For a man to wear a personal fedora would be to reject the fedora headship Christ provides.
Unfortunately, this theory has no merit. The fedora, with its soft brim and characteristic shape, was named after Fédora, a character in an 1882 play of that name staring Sarah Bernhardt. The daughter of a French courtesan, Bernhardt was an internationally known actress who often played male roles including Napoleon's son and Hamlet. In fact, fedoras were first worn primarily by women until Edward, a friend of Bernhardt's, discovered them in 1924. You know Edward—the short-termed king of England who abdicated after marrying an American divorcee. Or, possibly, so he wouldn't be outed as a Nazi.
At any rate, the "fedora headship of Christ" theory started as men, inspired by a French actress who played male roles, started wearing fedoras. Ultra-fundamentalists in the United States told their congregations that a man wearing a fedora was cross-dressing. Their sermons failed, however, and today more men than women wear them.
Men understood that a fedora did not
cover men with womanhood. Or even woman-playing-manhood. Hats aren't like the
federal headship of Christ that covers believers with Christ's righteousness. They're just hats.