Christian Heresies of the
Eleventh Century:

The Great Schism: Orthodox-Roman Catholic:
    The immediate issue was the "filioque clause", that "the Holy Ghost proceeds "from the Father and the Son" ("filioque"), says the Catholics, and  the Orthodox claim "from the Father alone" . But the key issue was that the Orthodox denied the supremacy of the Pope. The Roman Catholic Church maintains that the Pope the successor of Peter, the head of the entire Church before the split and after the Schism.
    The "official" schism in 1054 was the excommunication of Patriarch Michael Cerularius of Constantinople, followed by his excommunication of the pope's representative.
    The personal excommunications were mutually rescinded by the Pope and the Patriarch of Constantinople in the 1960s, although the schism is not at all healed.   
    One sometimes sees it asserted either that the Eastern Orthodox Church or the Roman Catholic Church was founded at the time of this great schism. That is false. The One Holy Catholic and Apostolic Church was ruled by five patriarchs: those of Rome, Constantinople, Antioch, Alexandria, and Jerusalem, each having authority over bishops in a specified geographic territory. Although the five split from each other, none was a newly founded organization. Each group took (and still today takes) the view that it is the One Holy Catholic and Apostolic Church and the other group left that church at the time of the schism.

    The "Pope":
    - The Orthodox do not accept the supremacy of the Pope, as the only successor of Peter.
    - The Orthodox do not have a central authority, no one even claims to be the successor of "Peter", with the immense authority given to him, and only to him and his successors!, by Jesus in Matt.16, Jn.21, Acts.1-9.,
    - If the Orthodox could accept the authority of the Pope, as the successor of Peter, all the other differences would be immediately eliminated.
    David and Peter: The shepherds of the People of God:
    Jesus did with "Peter" what God had done with "David":
    1- In Ezekiel 34 God says repeatedly "I myself will look after and tend my sheep"... "I myself will pasture my sheep" (34:11-15)... but in verse 23, God says: "I will appoint one shepherd over my sheep to pasture them, my servant David; he shall pasture my sheep and be their shepherd"... and so, he who is loyal to David or his successors, belongs to the People of God, and he who is not loyal to David or his successors, does not belong to the People of God, even if he is a Jew born in Jerusalem, rather he is a rebel, or a heretic ("heretic" means "rebel")
    2- Jesus did the same: In John 10 he repeats "I am the shepherd... I am the good shepherd"... but in John 21, after resurrection, Jesus says 3 times to Peter, and only to Peter, in front of the other Apostles, "feed my lambs... tend my sheep... feed my sheep" (John 21:15-17)... "my lambs"... "my sheep"... the lambs and sheep of Jesus!... so now, accordingly, he who is loyal to Peter or his successors, belongs to the only Church of Christ, and he who is not loyal to Peter or his successors, does not belong to the Church of Christ, even if he knows all the Bible by heart, he is a rebel, or a heretic...
    The Primacy of Peter in the NT:
    "Peter" was chosen by Jesus to be the "leader" of the 12, and of the whole Church of Christ:
        - In Matt.16, Jesus promised Peter the primacy
        - In John 21, Jesus gave it to him.
        - In Acts, Peter exercised it.
    1- In Matt.16:19: "I will give you, Peter, the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven".
    Here, Jesus offers to Peter, 2 things:
        1- Jesus offers Peter, and only to Peter, the "keys of the kingdom", in front of the other 11 Apostles.
        2- Jesus promises Peter "infallibility"... if whatever he binds or looses on earth, shall be bound or loosed in heaven, it is because whatever he binds or looses it is the truth, "infallible", "without any possibility of error"!.
    A friend of mine told me, it is impossible, because no one is infallible on earth... but then, he agreed with me that when Matthew or Solomon wrote the Bible, they were "infallible", it is the word of God!... so, hundreds of people were infallible, when they wrote the Bible!...
   ... And to John, Luke, or David, God did not promised infallibility to write the Bible... but to Peter, Jesus promised directly "infallibility", in whatever he binds or looses on earth!...
   ... The Holy Spirit who inspired the authors of the Bible, is the same one who inspires Peter when he binds or looses on earth!.
    2- In John 21:15-17:In his last apparition to the Apostles after resurrection, "Jesus said to Simon Peter... feed "my" lambs... a second time... tend "my" sheep... the third time... feed "my" sheep"...
    The other Apostles were there, but only to Peter Jesus gave the order: Feed and tend my lambs and sheep... "my" sheep!... those of Jesus!.
    3- In Acts: Peter exercises his "supremacy". He is the one talking, when all the Apostles are present. The first 11 chapters of Acts, report 8 rather long sermons of Peter (1:15, 2:14, 3:12, 4:8, 5:29, 8:20, 10:34, 11:4).
    - Another important fact in Acts:
    When Judas died, the other Apostles decided to name one to do the job Judas was supposed to do, "to take the place in this ministry and apostleship which Judas abandoned... and they choose Matthias, who was added to the 11 apostles" (Act.1:15-26)... you can be sure that when Peter died, the other apostles did the same, they choose one to do the job Peter was supposed to do... the actual Pope John Paul II is the 262 successor of Peter... and the Catholic Church is the only one to claim a successor of Peter!.

Orthodox   "Organization of the Church".