This should be the focus of the discussions between the East and the West, not whether the pope has any jurisdiction in the first place. The Orthodox overstate their position when they deny that their is any inherent jurisdiction or that it is only a question of "honor". Their are two foci of authority in the Church, the pope and the college of bishops. This is clearly shown in the history of the early Church. That there should be tension between these two foci is not surprising, just as it was not surprising that there was tension in understanding the two natures of Christ. Remember that heresy is mostly based on trying to remove the tension between two competing truths, e.g., Jesus is God, Jesus is man. The orthodox, and true, position is that he is both. This may seem clear to us today but it was, as we all know, a cause of strife in the early Church. In a like manner, we should try to reconcile the two truths that the pope is a focus of authority and that the college of bishops is a focus of authority, without trying to pit one against the other.
The idea that this jurisdiction is biblical was pressed by Pepe St. Leo I (Great), as the "ruler" of the Church.
Actually, the idea of the pope as successor of St. Peter can be documented to go back at least to the time of Pope Stephen I. More importantly, this claim (clearly and repeatedly made even in church councils) was never denied, even by the Eastern bishops, before 1054.
I don't know where you are getting "in the first place" as my statement doe snot question if the Bishop of Rome has jurisdiction, but what extent and nature of that jurisdiction is.
When I wrote "We do not agree on what that jurisdiction means" it is hardly a denial of its existence.
The Orthodox overstate their position when they deny that their is any inherent jurisdiction or that it is only a question of "honor".
And the Catholics certainly overstate it. I am sure you are familiar with the Catechism of the Catholic Church which states in paragraph 882
The undivided Church certainly never adhered or accepted such definitions.
St. Peter certainly never claimed it, and the Holy Apostles never acted towards him as if he were their ruler.
The issue of honor was never solitary. Ecclesial honor and privilege were granted by the bishops to those Bishops in Apostolic Sees (the Five Patriarchates), beginning with Rome based on the imperial majesty of the city, and that also inlcuded jurisdiction within the given patriarchate.
No Ecumenical Council argued for Papal supremacy based on Matthew 16.
Their are two foci of authority in the Church, the pope and the college of bishops. This is clearly shown in the history of the early Church. That there should be tension between these two foci is not surprising, just as it was not surprising that there was tension in understanding the two natures of Christ.
I find that to be a very poor example. The Holy Apostles were given the same keys in Matthew 18. There were no two foci of authority among them, although when St. Peter spoke, others listened. But he did not lord over any of his apostolic brethren.
Actually, the idea of the pope as successor of St. Peter can be documented to go back at least to the time of Pope Stephen I
That is in th latte part of the 3rd century. In other words, the earliest claim was some 230 years after the Pentecost.