This is an old argument. There were men in the Bible who were said to have had long hair. Jehovah forbad Samson to cut his hair and David's son, Absalom, was said to have cut his hair once annually when it became a burden to him. Absalom clearly wore his hair as he saw fit and cut it when it became too long to deal with, perhaps interfering with his battle helmet's fit. Though Absalom is said to have been "hanged" by his hair having been caught in a tree, the Bible gives no indication that God was displeased with Absalom's wearing long hair.
The argument is old, but old doesn't mean it is inaccurate.
Samson was under a Nazirite vow by the command of God, as was John the Baptist, by the way. The Nazirite vow had three requirements, one of which was that the hair was cut at the beginning and at the end of the vow. Since Samson was under the vow for life, of course, he wasn't supposed to cut his hair -- but the point is that he was an exception to the norm. The reason it was unusual is that people did normally cut their hair.
The statement Paul made in I Corinthians 11 deals with the general. "Does not even nature itself teach you that if a man has long hair, it is a dishonor to him?" (I Corinthians 11:14). A general truth is not defined by exceptions.
Then too, the Nazirite vow was a part of the Law of Moses. It is not a part of the Law of Christ. The exception no longer exists. Thus to claim God wanted Samson to have long hair doesn't lead to the conclusion that all men or even some men are to have long hair.
Absalom is an example of a rebellious son. He overthrew David's kingdom and had himself enthroned. To hold him up as the poster boy for long hair is to prove the point made in the article. True, God did not say pro or con about Absalom's hair length. The fact of it was simply noted. Similarly, Abraham lied on two occasions. At the time God doesn't say pro or con about Abraham's lies, but we don't conclude that He accepted them. We know from other passages that lying is wrong. In the same way, just because nothing is said at the time concerning Absalom's hair length, we cannot conclude that it was accepted. We would have to look elsewhere for God's opinion on the matter.