I think you will find the answer here because it raises the same question:
His words in the above passages, as well as in other passages concerning head coverings (cf. I Cor. 11: 4-7), are directed to laymen, not clergy. In other passages Saint Paul makes an obvious distinction between the clerical and lay rank (cf. I Cor. 4:1, I Tim. 4:6, Col. 1:7, and others).
He did not oppose the Old Testament ordinance in regard to hair and beards since, as we have noted above, he himself observed it, as did Our Lord Himself, Who is depicted on all occasions with long hair and beard as the Great High Priest of the new Christian priesthood."
So important had this pagan custom be come for Roman clergy by the 11th Century that it was listed among the reasons for the Anathema pronounced by Cardinal Humbert on July 15, 1054 against Patriarch Michael in Constantinople which precipitated the Western Church's final falling away from the Orthodox Church: "While wearing beards and long hair you [Eastern Orthodox] reject the bond of brotherhood with the Roman clergy, since they shave and cut their hair." [!]
Yikes! That seems a little harsh. :) Do you give any credence to that, or was this guy just bloviating? :)