Cyril of Alexandria was the real influencial theologian behind Chalcedon, not Leo I, bishop of Rome

Ruins from ancient Chalcedon(Today: Kadikoy), across the waters from ancient Constantinople (today Istanbul) across the entrance of the Bosphus straight, modern Turkey. 

Ruins from either a tower wall or, according to a sign there that I have seen myself (in Turkish- I can read some of it and had help with other friends in translating more of it.), an ancient water depot in Kadikoy, Turkey, which was called Chalcedon where the Fourth Ecumenical Council was held in 451 AD.   The Turks are restoring it right now and explain this is from "Eski Kadikoy" (ancient Kadikoy) and "Byzantion" and the Turks call it "Kalkedon".  

I am enjoying listening to and watching the Boston College Debate about the Papacy with James White and Rob Zins for the Protestant position vs. Robert Sungenis and Scott Butler for the Romanist position.  I had seen Scott Butler's meltdown before, but never the full debate.  

Dr. White included some information that up until now, I was not aware of, about the Council of Chalcedon, Leo I, and Cyril of Alexandria. (around the 2 hour, 6 minute mark) So I googled around and found the details from William Webster (I should have known!).  Below is a portion of a larger article by William Webster, in defending against Roman Catholic Steve Ray's claims.

This again proves that there was no such thing as a Papacy in the early centuries, and even Leo I, cannot really claim to be the "first Pope".    Many church history textbooks, unfortunately, are misleading and anachronistic, by writing things like, "Pope Leo I" or "Leo I, the first Pope" or  "Gregory the Great, bishop of Rome from 590-604 AD, the first Pope".  Even Gregory in 601 AD did not claim to be univeral bishop and in fact rebuked John of Constantinople for making such a claim. Gregory wrote the the Emperor Maurice:  "Now I confidently say that whosoever calls himself, or desires to be called, Universal Priest, is in his elation the percursor of AntiChrist, because he proudly puts himself above all others.  ( Gregory I, bishop of Rome, 590-604 AD; Book VII, Epistle XXXIII)

From William Webster's article:

The Council of Chalcedon
Peter Has Spoken Through Leo
Steve Ray asserts that the early councils give evidence to their belief in papal primacy. He gives the example of the fathers at Chalcedon who proclaimed ‘Peter has spoken through Leo’ as a result of examining Leo’s Tome, his doctrinal defense of the Trinity and the nature of Christ. The impression given by Roman apologists to this proclamation of the fathers at Chalcedon is one of blind submission to the doctrinal teachings of the pope. Such is not the case. In fact, just the opposite. What is rarely ever explained by these apologists is that Leo’s Tome and its doctrinal teaching was only accepted by the Council when it was thoroughly analyzed and determined not be in conflict with the teaching of Cyril of Alexandria. John Meyendorff gives the following helpful information on Leo and Chalcedon:  (my emphasis and coloring) 

Leo did not participate personally in the council, but his legates at Chalcedon carried with them another remarkable letter addressed to the assembled fathers and expressing the pope’s wish that ‘the rights and honor of the most blessed apostle Peter be preserved’; that, not being able to come himself, the pope be allowed ‘to preside’...at the council in the persons of his legates; and that no debate about the faith be actually held, since ‘the orthodox and pure confession on the mystery of the Incarnation has been already manifested, in the fullest and clearest way, in his letter to bishop Flavian of blessed memory.’ No wonder that his legates were not allowed to read this unrealistic and embarrassing letter before the end of the sixteenth session, at a time when acrimonious debates on the issue had already taken place! Obviously, no one in the East considered that a papal fiat was sufficient to have an issue closed. Furthermore, the debate showed clearly that the Tome of Leo to Flavian was accepted on merits, and not because it was issued by the pope. Upon the presentation of the text, in Greek translation, during the second session, part of the assembly greeted the reading with approval (‘Peter has spoken through Leo!’ they shouted), but the bishops from the Illyricum and Palestine fiercely objected against passages which they considered as incompatible with the teachings of St Cyril of Alexandria. It took several days of commission work, under the presidence of Anatolius of Constantinople, to convince them that Leo was not opposing Cyril. The episode clearly shows that it was Cyril, not Leo, who was considered at Chalcedon as the ultimate criterion of christological orthodoxy. Leo’s views were under suspicion of Nestorianism as late as the fifth session, when the same Illyrians, still rejecting those who departed from Cyrillian terminology, shouted: ‘The opponents are Nestorians, let them go to Rome!’ The final formula approved by the council was anything but a simple acceptance of Leo’s text. It was a compromise, which could be imposed on the Fathers when they were convinced that Leo and Cyril expressed the same truth, only using different expressions (John Meyendorff, Imperial Unity and Christian Division (Crestwood: St. Vladimir’s, 1989), p. 155-156.).

Chalcedon Rejects Leo's Demands
The fact that the Coucil of Chalcedon did not subscribe to the theory of papal supremacy as espoused by Vatican I is also seen in its acceptance of the 28th canon in which it refused to submit to the demands of pope Leo I. The following is a brief history of this incident taken from The Matthew 16 Controversy:

The papal legates strenously objected to the passage of canon 28 and Leo, the bishop of Rome, refused to accept it. However, the Council refused to acquiesce to papal demands and received the canon as valid, overriding the papal objections. As Meyendorff states:

The commissioners bluntly declared the issue closed—‘All was confirmed by the council,’ they said—explicitly denying any papal right of veto (John Meyendorff, Imperial Unity and Christian Division (Crestwood: St. Vladimir’s, 1989), p. 183).

W.H.C. Frend comments:

By Canon 28 not only were the decisions in favor of Constantinople as New Rome ratified, but its patriarchal jurisdiction extended into Thrace on the one hand, and Asia and Pontus in Asia Minor on the other. The legates were not deceived by the primacy of honor accorded to Rome. They protested loud and long. The Council, however, had decided, and the decision of the Council was superior to the wishes even of the Bishop of Rome (W.H.C. Frend, The Early Church (Philadelphia: Fortress, 1965), p. 232).

Even though Leo rejected this canon—and the Eastern bishops eagerly sought his approval— his nonacceptance did not affect the validity of the canon. As Robert Eno observes:

The easterners seemed to attach a great deal of importance to obtaining Leo’s approval of the canon, given the flattering terms in which they sought it. Even though they failed to obtain it, they regarded it as valid and canonical anyway (Robert Eno, The Rise of the Papacy (Wilmington: Michael Glazier, 1990), p. 117).

From a jurisdictional standpoint it is clear that Nicaea, I Constantinople and Chalcedon do not support the teaching of Vatican I on papal primacy. After pointing out that Chalcedon refused to submit to the demands of the Bishop of Rome, Frend sums up the historical reality of the ecclesiology of the patristic age with these observations:

So ended Chalcedon. The Church was still the Church of the great patriarchates, maintaining an equilibrium in respect of each other, whose differences could be solved, not by the edict of one against the other but by a council inspired and directed if no longer presided over by the Emperor. It was a system of Church government opposed to that of the papacy, but one which like its rival has stood the test of time (W.H.C. Frend, The Early Church (Philadelphia: Fortress, 1965), p. 232).

The fact that the Council fathers at Chalcedon received canon 28 as valid in direct opposition to papal demands demonstrates conclusively that papal primacy was not an historical reality at that time. Some have asserted, however, that because the Eastern bishops sought Leo’s confirmation of the canon, this proves that they implicitly acknowledged the primacy of the Bishop of Rome. Herbert Scott, for example, states:

Impartial examination of this celebrated XXVIIIth Canon of Chalcedon and its circumstances...shows that instead of depreciating papal claims it supports them...The Headship of Rome is shown and confessed in the very act of the bishops of this fragment of a council trying to obtain Leo’s confirmation of their canon (S. Herbert Scott, The Eastern Churches and the Papacy (London: Sheed & Ward, 1928), p. 199).

While it is true that the Eastern bishops sought Leo’s confirmation of canon 28, it is not true to assume their belief in papal primacy. This is demonstrated from a very simple historical reality: The bishops did not submit to papal demands. They sought Leo’s confirmation, even using strongly primatial language in their appeals to him, but in the end they received the canon as valid despite his continuing opposition. The early Church greatly valued unity and sought it whenever possible. This was the desire of the bishops of Chalcedon in trying to obtain a unanimous decision regarding canon 28. However, the lack of confirmation by the Bishop of Rome did not prevent this canon from becoming ratified and received into the canon law of the Eastern Church and eventually that of the West as well. From a jurisdictional standpoint, therefore, it is clear that neither Nicaea, I Constantinople nor Chalcedon support the teaching of Vatican I on papal primacy.

W.J. Sparrow–Simpson likewise affirms the fact that the history of Chalcedon proves that the early Church held to a view of Church government which was antithetical to that formulated by the Roman Bishops and Vatican I:

What was the true relation of the Pope and the Council to each other? How was it understood in primitive times? Did the Collective Episcopate regard itself as subordinated, with no independent judgment of its own, to decisions of the Roman authority? Or was the Council conscious of possessing power to accept or refuse the papal utterances brought before it? Bossuet maintained that the treatment of Papal Letters by the early General Councils afforded convincing proof against their belief in any theory of papal in errancy. The famous letter of Leo to Flavia was laid before the Council of Chalcedon in the following terms: ‘Let the Bishops say whether the teaching of the 318 Fathers (the Council of Nice) or that of the 150 (Constantinople) agrees with the letter of Leo.’ Nor was Leo’s letter accepted until its agreement with the standards of the former Ecumenical Councils had been ascertained. The very signatures of the subscribing Bishops bears this out—‘The letter of Leo agrees,’ says one, ‘with the Creed of the 318 Fathers and of the 150 Fathers, and with the decisions at Ephesus under St Cyril. Wherefore I assent and willingly subscribe.’ Thus the act of the Episcopate at Chalcedon was one of critical investigation and authoritative judgment, not of blind submission to an infallible voice (W.J. Sparrow Simpson, Roman Catholic Opposition to Papal Infallibility(London: John Murray, 1909), p. 28) (The Matthew 16 Controversy, pp. 177-179, 181).

William Webster