Well, first, the mitre is not unique to the Pope. They are ceremonial headpieces for Bishops. The pope, as Bishop of Rome, also may wear one. If you look at Benedict XVI's and Pope Francis' papal coat of arms, they actually are the first two popes to include a mitre rather than a papal tiara.

Some argue that the mitre can be traced all the way back to the apostles that lived and worked with Jesus, but is most definitively traced back to a Papal Bull from Pope Leo IX in the 11th century. He, without explaining what a mitre is for, mentions that a newly ordained bishop needs to be sent one. This shows that they were probably in common use for a decent amount of years before that.

The current design apparently has origins from a similar Byzantine headpiece, but I admittedly don't know much about that portion.

I don't know if I helped answer your question, so please feel free to inquire more and I'll answer what I can. To back up the information I gave you here, and find more information, search "Mitre" on the New Advent Catholic Encyclopedia. There is a free, online edition. It will also give suggestions for further reading if you check out the references for its entries.

Can I piggyback this and ask why hats and covering of the head is such a sticking point in Christianity and Islam?

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