JewsAndJoes.com

I Corinthians 11:14-15
(14)  Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?
(15)  But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.

Before the main question is really answered, lets ask a couple prerequisite questions.

Did the Apostle Paul have the authority to add new commandments which are not already prescribed in the Written Torah of Moshe (Moses)? And did the Apostle Paul have the authority to contradict verses in the Written Torah which clearly permit long hair on men, such as with the Nazirite vows (Numbers 6:1-21)?

Both of those questions can largely be answered by the following:

Deuteronomy 4:2 "You shall not add to the word which I am commanding you, nor take away from it, that you may keep the commandments of יהוה your Elohim which I command you."

Deuteronomy 12:32 "Whatever I command you, you shall be careful to do; you shall not add to nor take away from it"

Now back to I Corinthians 11:14

What does the verse actually say in the Greek text?

1 Corinthians 11:14-15
(14)  Doth^(G2228) not even^G3761 nature^G5449 itself^G846 teach^G1321 you,^G5209 that,^G3754 if^G1437 a man^G435 have long hair,^(G2863) it is^G2076 a shame^G819 unto him?^G846
(15)  But^G1161 if^G1437 a woman^G1135 have long hair,^G2863 it is^G2076 a glory^G1391 to her:^G846 for^G3754 her hair^G2864 is given^G1325 her^G846 for^G473 a covering.^G4018

G2863
κομάω
komaō
kom-ah'-o
From G2864; to wear tresses of hair: - have long hair.

G2864
komē
kom'-ay
Apparently from the same as G2865; the hair of the head (locks, as ornamental, and thus differing from G2359, which properly denotes merely the scalp): - hair.

G2359
θρίξ, τριχός
thrix  trichos
threeks
Of uncertain derivation; hair: - hair. Compare G2864.

The author of 1 Corinthians 11:14 was likely referring to the Greek custom of women who would pile their hair on top of their heads, braiding and tressing it with ornate hairpins of gold, silver, and precious jewels. In our modern culture, it has become less common, but still seen where woman will decorate their hair in all kinds of styles and designs, but to see a man as such would certainly be taboo. Men with long hair generally keep it very plain, pulled back, or disgustingly unkept and manly (insert grin of sarcasm)... and it is likely that men in antiquity also had similar customs, as ancient artwork often confirms. For example, men of war are frequently depicted with long head and facial hair from regions as far as ancient Japan and China to Germania and Britannia. Even the early Roman period had men commonly wearing long hair and beards.

The New Paradigm

This new redefining, religiously-charged, custom of pressuring men to have short hair and clean-shaven faces in order to be seen as an upright and stable citizen is an intensely inaccurate and misleading reality not shared with most all of our ancestors, including those in Ancient Israel (noting the Nazirite vows of elevated righteousness). To some degree, this modern paradigm is likely a product of the Hippie culture of the 60s, where the "free love and sex movement" was predominantly depicted by men with long hair and beards, later to be carried into the Heavy Metal drug and music scene of the 70s and 80s (where the beard seems to have been lost, but long hair kept). 

In conclusion, we should be careful not to let our modern cultures define what is truly right and acceptable. The Torah should define much of these things for us, and if it is NOT in the Torah, then apparently it was considered permissible to the Most High, the Creator of the Universe. In this case, no where in the Written Torah does it forbid men to have long hair. And conversely, no where does it forbid women from having short hair.

Be ever mindful not to ADD to the Torah!