Roman Catholic apologist and historian, Steve Weidekopf, wrote the following about Pope Leo I, Chalcedon, and the early evidence for papal primacy:
[Papal primacy] was perhaps most resoundingly affirmed by the 500 bishops meeting at the Council of Chalcedon in 451 to discuss the heretical teachings of Eutyches (378-454). After reading out loud the Tome of Pope St. Leo I the Great (r. 440-461), in which he asserted the incompatibility of Eutyches’s teachings with the orthodox faith, the bishops declared in union, “thus through Leo has Peter spoken!” (Steve Weidenkopf, The Real Story of Catholic History: Answering Twenty Centuries of Anti-Catholic Myths [El Cajon: Catholic Answers, 2017], 226)
Firstly, it should be noted that this event from Chalcedon does not prove the later dogmatic teachings of Vatican I vis-à-vis the Papacy (on this, see Pastor Aeternus [1870]).
Anglican theologian, Edward Denny, writing in response to Leo XIII’s encyclical on the authority of the Papacy, Satis Cognitum (1896), wrote the following about the bishops’ declaration in Chalcedon:
The fautors of Papalism, however, are fond of appealing to the exclamation of the Fathers of the Synod when 'The Tome' was read at the second session of this Council, as is done by the Satis Cognitum itself. Did not the Fathers, it is said, with an air of triumph, say: 'Peter has spoken by Leo,' and does not this statement prove that they ascribed to it that authority which the Vatican Decrees declare to belong in virtue of his Apostolic Primacy, jure divino to the bishop of Rome. To this it is to be replied--(a) it is irrational to adduce an 'exclamation' of the Bishops as authoritative, as a Synod embodies its synodical declarations in Canons, Decrees, or other formal Acts; (b) next, the absurdity of making this use of the words in question is apparent from the text of the 'exclamation' of which they form a part. 'This is the faith of the Fathers, this s the faith of the Apostles; we all believe thus, the Orthodox believe thus, anathema to him who does not believe thus; Peter has spoken by Leo; the Apostles taught thus, Leo's doctrine is pious and true, be the memory of Cyril eternal, Leo and Cyril teach the same. Why was not this read at Ephesus? This is what Dioscurus concealed.
The Fathers here couple St. Leo's teaching with that of St. Cyril as a proof that the former is orthodox, as being identical with that of the latter. Such a proceeding on the part of the Fathers would have been presumptuous in the highest degree if Papalism was true, nay, more blasphemous, as involving a denial of the position belonging to the Roman Bishop by the institution of Christ in the Divine Constitution of the Church. The words, 'Peter has spoken by Leo,' have a much simpler meaning, viz., that St. Leo's letter contained and taught that faith in the Incarnation which St. Peter had first proclaimed as that of the Apostles in answer to the memorable question which our Lord addressed to them as Caesarea Philippi, as indeed the Fathers themselves say in their decree concerning the faith. They would be true of any Bishop or Pastor who teaches in accordance with that glorious confession and would be held to be, in the fifth century, especially appropriate to express the orthodoxy of the letter of the one who occupied the See which by that time was universally supposed to have been founded by St. Peter. (Edward Denny, Papalism: a treatise on the claims of the papacy as set forth in the encyclical Satis Cognitum [1912], 215 § 458-59)
To study the overwhelming evidence against the dogmatic teachings of the papacy in Roman Catholicism, one should pursue Denny's book. It remains unanswered by Catholic apologists and historians even to this day.