Why it is that, even among non-Christians, men are looked down on for having long hair?
What harm does it do? Nothing. Not one thing at all. I've yet to see one even a slightly logical argument against men having long hair. It could even be said that looking down on men for having long hair is hypocritical because women aren't looked down on as much for having short haircuts (I'm referring to your average woman's short haircut, not a buzz cut).
I feel like I Corinthians 11:14, that says, "Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?" is something that a man, Paul, wrote, and not something that God said, He was writing based on the culture of that day, not about any real moral basis on why men shouldn't have long hair. All he says is that it's a shame for men to have long hair.
Paul was addressing the carnality of the Christians in Corinth - it wasn't what they did, it was why they were doing it. Having long hair doesn't hurt women and the only time it's hurt men is just people thinking less of men who have long hair, which is basically stereotyping and discriminating based on appearance. I seriously doubt that God is going to send a man to hell just because he has long hair.
It is interesting that you quote I Corinthians 11:14 as being applicable to your question, but you dismiss it as the words of a man and not God. Upon what do you base this conclusion -- besides your rejection of what is stated?
In regards to the things that he taught, Paul said, "But I make known to you, brethren, that the gospel which was preached by me is not according to man. For I neither received it from man, nor was I taught it, but it came through the revelation of Jesus Christ" (Galatians 1:11-12).
In the opening thoughts of I Corinthians Paul made this observation:
"And I, brethren, when I came to you, did not come with excellence of speech or of wisdom declaring to you the testimony of God. For I determined not to know anything among you except Jesus Christ and Him crucified. I was with you in weakness, in fear, and in much trembling. And my speech and my preaching were not with persuasive words of human wisdom, but in demonstration of the Spirit and of power, that your faith should not be in the wisdom of men but in the power of God. However, we speak wisdom among those who are mature, yet not the wisdom of this age, nor of the rulers of this age, who are coming to nothing. But we speak the wisdom of God in a mystery, the hidden wisdom which God ordained before the ages for our glory, which none of the rulers of this age knew; for had they known, they would not have crucified the Lord of glory. But as it is written: Eye has not seen, nor ear heard, Nor have entered into the heart of man The things which God has prepared for those who love Him." But God has revealed them to us through His Spirit. For the Spirit searches all things, yes, the deep things of God. For what man knows the things of a man except the spirit of the man which is in him? Even so no one knows the things of God except the Spirit of God. Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God. These things we also speak, not in words which man's wisdom teaches but which the Holy Spirit teaches, comparing spiritual things with spiritual. But the natural man does not receive the things of the Spirit of God, for they are foolishness to him; nor can he know them, because they are spiritually discerned. But he who is spiritual judges all things, yet he himself is rightly judged by no one. For "who has known the mind of the LORD that he may instruct Him?" But we have the mind of Christ" (I Corinthians 2:1-16).
Paul clearly states that his teaching is not his own, but God. He further claims that what he teaches is not based on human wisdom. He also warned that people would reject these teachings because they prefer worldly ideas over godly ideas.
Paul continues this point throughout the book of I Corinthians. He knew that he was making difficult points. After teaching that women were to be silent in the worship service, he presented this challenge: "If anyone thinks himself to be a prophet or spiritual, let him acknowledge that the things which I write to you are the commandments of the Lord" (I Corinthians 14:37). Therein lies the answer. Are you willing to accept that Paul is teaching the Lord's commands or are you going to say he is lying? You can't have it both ways.
By the way, Peter also confirms that Paul's writings were inspired by God when he said, "Therefore, beloved, looking forward to these things, be diligent to be found by Him in peace, without spot and blameless; and consider that the longsuffering of our Lord is salvation--as also our beloved brother Paul, according to the wisdom given to him, has written to you, as also in all his epistles, speaking in them of these things, in which are some things hard to understand, which untaught and unstable people twist to their own destruction, as they do also the rest of the Scriptures" (II Peter 3:14-16). Peter called Paul's writing "Scriptures," which means sacred or inspired writings.
Until you come to grips with the fact that Paul was recording the words of God, I cannot address the rest of your points because the foundation is too far apart.
However, I will make a short point as to why non-Christians generally look on long hair with disfavor. Choice of clothing, including hairstyles, are selected by individuals to make statements about themselves. You might want to deny it, but it doesn't change the facts. I have an article in my files, written by Su Bacon of the Kansas City Star, which starts out with this line: "Clothes speak volumes about the people wearing them." She went on to make points about appropriate clothing selections for a job interview, noting that what a person selects for the interview will make a strong impact on whether they are hired. I have another article written by John T. Molloy in a syndicated column called "Dress for Success." This article was titled "Dress of Teens Could Signal Trouble." The point made was that the most common first indication of trouble with a teenager is seen in their change of attire. If you will grant me the point that dress makes a statement, then what statement does long hair on a man make?
Paul's point is that it is natural for men to favor short hair. Why? The answer is obvious. Men are creatures of action. Long hair gets in the way. It takes more time to properly care for. It can be a hindrance. It is hot. In fact, there is a classic example in the Old Testament. "Then Absalom met the servants of David. Absalom rode on a mule. The mule went under the thick boughs of a great terebinth tree, and his head caught in the terebinth; so he was left hanging between heaven and earth. And the mule which was under him went on" (II Samuel 18:9). Most commentators pin the reason for his entanglement on his long hair. "And when he cut the hair of his head - at the end of every year he cut it because it was heavy on him - when he cut it, he weighed the hair of his head at two hundred shekels according to the king's standard" (II Samuel 14:26).
So what does long hair say? It says that here is a man with time on his hands; here is a man who isn't very active. Long hair has consistently been seen as a sign of a rebellious attitude -- a person who doesn't want to go along with the crowd. All these "statements" do not display the Christian's goal of meekness, quietness of spirit, and hard work.