Now, the Vatican claims that Our Lord gave St. Peter the Keys to the Kingdom of Heaven.
And claims from that that St. Peter was the Head of the Apostles.
And claims that St. Peter founded the Church of Rome.
And claims that the Church of Rome retains exclusive possession of the Keys of St. Peter.
And claims that the Pope of Rome alone has the authority that St. Peter had through the Power of the Keys.
And since he alone has that authority, he has supremacy over the Church.
The odd thing is that the claim of Rome's authority on the basis of Matthew 16 comes rather late: the first allusion I think may be this letter of Pope St. Gregory the Great to the Emperor Maurice, whinning about the creation of the title "Ecumenical Patriarch."
To Mauricius Augustus.http://www.newadvent.org/fathers/360205020.htm
Gregory to Mauricius, etc.
Our most pious and God-appointed lord, among his other august cares and burdens, watches also in the uprightness of spiritual zeal over the preservation of peace among the priesthood, inasmuch as he piously and truly considers that no one can govern earthly things aright unless he knows how to deal with divine things, and that the peace of the republic hangs on the peace of the universal Church. For, most serene Lord, what human power, and what strength of fleshly arm would presume to lift irreligious hands against the lofty height of your most Christian Empire, if the concordant hearts of priests were studious to implore their Redeemer for you with the tongue, and also, as they ought to do, by their deservings? Or what sword of a most savage race would advance with so great cruelty to the slaughter of the faithful, unless the life of us, who are called priests but are not, were weighed down by works most wicked. But while we neglect the things that concern us, and think of those that concern us not, we associate our sins with the barbaric forces and our fault, which weighs down the forces of the republic, sharpens the swords of the enemy. But what shall we say for ourselves, who press down the people of God which we are unworthily set over with the loads of our sins; who destroy by example what we preach with the tongue; who by our works teach unrighteous things, and with our voice only set forth the things that are righteous? Our bones are worn down by fasts, and in our mind we swell. Our body is covered with vile raiment, and in elation of heart we surpass the purple. We lie in ashes, and look down upon loftiness. Teachers of humility, we are chiefs of pride; behind the faces of sheep we hide the teeth of wolves. But what is the end of these things except that we persuade men, but are manifest to God? Wherefore most providently for restraining warlike movements does the most pious lord seek the peace of the Church, and, for compacting it, deigns to bring back the hearts of its priests to concord. And this indeed is what I wish; and, as far as I am concerned, I render obedience to his most serene commands. But since it is not my cause, but God's, since the pious laws, since the venerable synods, since the very commands of our Lord Jesus Christ are disturbed by the invention of a certain proud and pompous phrase, let the most pious lord cut the place of the sore, and bind the resisting patient in the chains of august authority. For in binding up these things tightly you relieve the republic; and while you cut off such things, you provide for the lengthening of your reign.
For to all who know the Gospel it is apparent that by the Lord's voice the care of the whole Church was committed to the holy Apostle and Prince of all the Apostles, Peter. For to him it is said, Peter, do you love Me? Feed My sheep John 21:17. To him it is said, Behold Satan has desired to sift you as wheat; and I have prayed for you, Peter, that your faith fail not. And thou, when you are converted, strengthen your brethren Luke 22:31. To him it is said, You are Peter, and upon this rock I will build My Church, and the gates of hell shall not prevail against it. And I will give unto you the keys of the kingdom of heaven and whatsoever you shall bind an earth shall be bound also in heaven; and whatsoever you shall loose on earth shall be loosed also in heaven Matthew 16:18.
Lo, he received the keys of the heavenly kingdom, and power to bind and loose is given him, the care and principality of the whole Church is committed to him, and yet he is not called the universal apostle; while the most holy man, my fellow priest John, attempts to be called universal bishop. I am compelled to cry out and say, O tempora, O mores!
Lo, all things in the regions of Europe are given up into the power of barbarians, cities are destroyed, camps overthrown, provinces depopulated, no cultivator inhabits the land, worshippers of idols rage and dominate daily for the slaughter of the faithful, and yet priests, who ought to lie weeping on the ground and in ashes, seek for themselves names of vanity, and glory in new and profane titles.
Do I in this matter, most pious lord, defend my own cause? Do I resent my own special wrong? Nay, the cause of Almighty God, the cause of the Universal Church.
Who is this that, against the evangelical ordinances, against the decrees of canons, presumes to usurp to himself a new name? Would indeed that one by himself he were, if he could be without any lessening of others—he that covets to be universal.
And certainly we know that many priests of the Constantinopolitan Church have fallen into the whirlpool of heresy, and have become not only heretics, but even heresiarchs. For thence came Nestorius, who, thinking Jesus Christ, the Mediator of God and men, to be two persons, because he did not believe that God could be made man, broke out even into Jewish perfidy. Thence came Macedonius, who denied that God the Holy Spirit was consubstantial with the Father and the Son. If then any one in that Church takes to himself that name, whereby he makes himself the head of all the good, it follows that the Universal Church falls from its standing (which God forbid), when he who is called Universal falls. But far from Christian hearts be that name of blasphemy, in which the honour of all priests is taken away, while it is madly arrogated to himself by one.
Certainly, in honour of Peter, Prince of the apostles, it was offered by the venerable synod of Chalcedon to the Roman pontiff. But none of them has ever consented to use this name of singularity, lest, by something being given peculiarly to one, priests in general should be deprived of the honour due to them. How is it then that we do not seek the glory of this title even when offered, and another presumes to seize it for himself though not offered?
He, then, is rather to be bent by the mandate of our most pious Lords, who scorns to render obedience to canonical injunctions. He is to be coerced, who does wrong to the holy Universal Church, who swells in heart, who covets rejoicing in a name of singularity, who also puts himself above the dignity of your Empire through a title peculiar to himself.
Behold, we all suffer offense for this thing. Let then the author of the offense be brought back to a right way of life; and all quarrels of priests will cease. For I for my part am the servant of all priests, so long as they live as becomes priests. For whosoever, through the swelling of vain glory, lifts up his neck against Almighty God and against the statutes of the Fathers, I trust in Almighty God that he will not bend my neck to himself, not even with swords.
Moreover what has been done in this city on our hearing of this title, I have indicated in full to my deacon and responsalis Sabinianus. Let then the piety of my lords think of me as their own, whom they have always cherished and countenanced beyond others, and who desire to render obedience to you and yet fear to be found guilty in the heavenly and tremendous judgment, and, according to the petition of the aforesaid deacon Sabinianus, let my most pious lord either deign to judge this business, or to move the often before mentioned man to desist at length from this attempt. If then through the most just judgment of your Piety he should comply with your orders, even though they be mild ones, we shall return thanks to Almighty God, and rejoice for the peace granted through you to all the Church. But should he persist any longer in his present contention, we hold this sentence of the Truth to be already made good; Every one that exalts himself shall be humbled Luke 14:11; 18:14. And again it is written, Before a fall the heart is lifted up Proverbs 16:18. I however, rendering obedience to the commands of my lords, have both written sweetly to my aforesaid fellow priest, and humbly admonished him to amend himself of this coveting of empty glory. If therefore he be willing to hear me, he has a devoted brother. But, if he persists in pride, I already see what will follow:— that he will find Him as his adversary of whom it is written, God resists the proud, but gives grace unto the humble James 4:6.
St. Gregory makes a few inaccuracies (Chalcedon did not offer Rome the title "Universal Bishop," although her representatives signed "representing...the most blessed and Apostolic Leo of the Universal Church, Pope of the City of Rome" in Latin). But that's not my interest here: my interest is that Pope Gregory is basing his authority on being the successor of St. Peter and therefore inheritor of the power of the keys, and it seems to be the first time such a claim for the basis of Rome's authority is made, in 595.
Any other evidence of Rome claiming universal authority of the basis of Matthew 16, without reading the Vatican's interpretation of Matthew 16 into every mention of St. Peter, prior to this?