Why is the heavily advocated and gladly embraced doctrine of women’s head-covering absolutely against the Sovereign Will of God?
It is a testament against the churches that they base their teachings not on the teachings of the Lord but on the teachings of Balaams and Jezebels in their midst.  Just as John writes, 1 Jn 10, they race ahead literally leaving Christ and His teachings behind.  Just so that they can promote their self-righteous image, they will go to any lengths and even dare to pretend theirs is an all-inclusive obedience since they obey their false teachers.
 The legacy of unfaithfulness bestowed upon his sons by the first father is clearly visible right from the beginning of the Bible till its end so that it is impossible to deny it.   They stick out like sore thumbs because of their inconsistencies with the eternal and infallible Word of God.  Yet, just as it was with Eve, instead of turning to God for wisdom and clarity, they remain oblivious to Truth and invite the wrath of God.
With regard to the said doctrine, 2 Thess 2:2 will let one know and so be warned that even when Paul was living there were in circulation letters or reports purported to be from him.   Besides also that, “..His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction.” (2 Pet 3:16)
One has only to read the referred passages carefully and in entirety to realize where exactly the infiltrations begin.  It is that obvious!
Man has always been unfaithful with the Word of God entrusted to him from the beginning. It was the vainglorious man (Gen 2:23) who distorted the commandment and kept the female in the dark, causing her to sin against God.  Even though he was very much present there, he neither did anything to avert it nor stop himself from disobeying as soon as the opportunity presented itself. 
This is why the Spirit testifies against them : refer Hos 6:7, Isa 43:27, Ezek 2:3, Zech 1:2, Mal 3:7, Ps 78:57, Deut 32:18, Isa 29:13, 2 Pet 3:16b etc. etc. 
For instance, Jer 8:8, “How can you say, ‘We are wise, for we have the law of the Lord,’ when actually the lying pen of the scribes has handled it falsely?”
We must understand, this is the reason the Holy Spirit was sent to us.  So that, we may be taught by Him (Jn 6: 44 – 45) and be led into all truth by Him and Him Alone.
In this particular case, teachings such as hair is the glory of the woman, man is the head of the woman, stuff and nonsense, betray their falsehood.  Yet, why is the Truth so difficult to discern?? 
Is it a wonder then that the Spirit testifies against such as these who are nothing but advocates of flesh, Jer 2:11, ” …. My people have exchanged their Glory for worthless idols.”
Let us ask ourselves, is the man the head of the woman or even vice versa, when the Word of God clearly states Christ is the Head over everything (eg. Ps 110:1, Eph 1:22 Col 1:18, 2:10 etc.). And why Head?  Because only in Him is Truth.  Only He may lead us according to His perfect righteousness, only He may show the splendor of His holiness.  In short, literally and truly only He may transform our bodies into instruments of righteousness, so that we may learn to walk before Him by it.
HOW COULD or WHY SHOULD the uncovered head of a woman dishonor the man while the uncovered head of the man supposedly honors God?
It is obvious they do not heed the Spirit.  Will they not heed common sense either?   Can’t they see that head-covering symbolizes NOTHING BUT THE CURSED AND OPPRESSIVE AUTHORITY (Gen 3:16) OF THE MALE OVER THE FEMALE?  And why should the redeemed continue under their curses when the very word ‘redeemed’ means ‘belonging to God’ or ‘ransomed by God’?  If God has paid the price for you, why do you act like you belong to someone else?  And what a price?  Could you, even if you should so desire, ever hope to repay Him?  Yet, you refuse to have Him who is your rightful Head, who’d liberate you from all evil bondage so that you may reign with Him? 
Are you not disobeying and dishonoring God?  Has not God, once and for all, repudiated man’s old lie of Gen 2:23, and proven to you the Truth or the prophesy therein when He offered Himself to be the Holy and Perfect Sacrifice for your sins when He shed His own Blood and slept the brief sleep of death for you (eg. Matt 26:26-29)?
Haven’t you read what the Spirit teaches about preparing the Way of the Lord (Isa 40:3-5)?   And yet, this is how you  presume to go about it?   Don’t you know that Jesus has testified it is only in the Perfect Oneness of God we may testify for ourselves that God lives in us?  Refer Jn 17:21-25.
Therefore this is how the Spirit testifies against the lot of you who are nothing but advocates of flesh, read Ezek 13:18, “….This is what the Sovereign Lord says: WOE TO THE WOMEN WHO … MAKE VEILS OF VARIOUS LENGTHS FOR THEIR HEADS TO ENSNARE PEOPLE…”
And because you do these things and teach others to do the same, the retribution of God is made known since of old, Ezek 13:21, “I WILL TEAR OFF YOUR VEILS AND SAVE MY PEOPLE FROM YOUR HANDS, AND THEY WILL NO LONGER FALL PREY TO YOUR POWER. THEN YOU WILL KNOW THAT I AM THE LORD.”
To all those who will respond to the Spirit, learn from Mary Magdalene who was the first one to offer the perfect worship, whose deeds have been given the Godly renown and honor of being placed alongside the Gospel (Lk 7:44-46):
1.  Contrite spirit (symbolized by her tears with which she wet His feet),
2.  freed of all dominion and spiritual bondage (symbolized by the wiping of His feet with her obviously UNCOVERED hair),
3.  reconciled with God (symbolized by her kissing of His feet – Ps 2:12)
4.  and lastly by fragrant offering of thanksgiving, the fruit of one’s lips (symbolized by the expensive perfume that she poured on His feet). 
Let those who can understand, understand.  While the wicked will continue in their wickedness, the Spirit reminds, “..Let him who does right continue to do right; and let him who is holy continue to be holy.” (Rev 22:11b)