The Catholic Church, and its shaky claim to "apostolic succession" is based on a power grab supported by Constantine after the Council of Nicaea in 325 AD. Once the Emperor moved the capital, the See at Rome felt left behind while the balance of power shifted. Thus, they began insisting on their claim to be "first among equals," with privileges based on the contrived idea that Peter is the "Rock" who owns the "keys of the kingdom."
If you look again with fresh eyes at Matthew 16:15-20, you can see that the Rock upon which Jesus is building his Church is the plain, clear declaration that Simon Peter just spoke. "Thou art the Christ, the Son of the Living God." Peter got a nickname for being the first to say it right. Simply change the usual punctuation, which is not in the original Greek manuscripts, and read: "And I also say to you that you are Peter. And on this rock I will build My church, and the Gates of Hell shall not withstand it." Peter is not the only one here. Jesus is speaking to all of his disciples.
They are at the foot of Mt. Hermon, above Caesareae-Philippi, standing within sight of a huge cave dedicated to the worship of Pan, one of the gods of the Graeco-Roman pantheon. It is a place full of false gods and demons. In this immediate context, the Keys of the Kingdom are related to the binding of demons and loosing of oppressed souls who have been subject to the old gods up until Jesus' arrival. They are given to all of the disciples collectively, just like when He sent out the seventy to proclaim the arrival of the Kingdom, and they returned praising God that they had been able to cast out demons in Jesus' name. This is a declaration of spiritual warfare, meant to go throughout the Roman Empire.
Thus, the claim to the Primacy of the Roman See is a spurious (dare I say "deliberate"?) misinterpretation of the Gospel intended to legitimize a power grab and establish an unwarranted authority over the other leading strands of the Church.
None of the other primary cities ever accepted the "Chair of Peter" as having a claim to superiority. The "Rock" is the declaration of faith that Jesus is the Christ, the Son of the Living God, and the keys were given to all of the disciples as a group. They are all alike commissioned to carry the Gospel to the world, and without the keys, none of them would have been authorized to start new assemblies of believers.
The Gospel of Christ's life, death and resurrection, teaching the Way to live as a Christian, familiarity with Jesus and the Eucharist, and obedience in accord with the Holy Spirit in one's heart, these are the essential keys to open the doors for sinners to repent and enter the Kingdom of Heaven.
It was only after the Apostolic Fathers passed away that Imperial politics allowed Roman Catholicism to gain credence, and then only because no one who knew the apostles still lived to refute it. Later, it came as no surprise when Rome's arrogance unilaterally added to the creed and tried to impose consensus that the dispute ended in schism. Regardless of the plain fact that the filioque is clearly a straight deductive conclusion drawn directly and solely from Scripture, the other Sees should have been consulted and had the problem of Arianism pointed out as the necessity of the addition. It was a matter of due respect, which was high-handedly disregarded. Today, the Orthodox Church allows it, but they don't say it in their liturgical creed.
Simply put, no one See can claim to have the only correct hermeneutic for interpreting the Bible. We have to have freedom to understand doctrines according to the light given us by the Holy Spirit as supported by Scripture. The completion of the Canon is the universal basis of the Christian Church, along with the consensus agreements documented by the various "full" ecumenical councils. Without the attendance of the Orthodox, Coptics, Armenians, and all who attended Nicaea, and now including Protestant representatives, no council can be truly ecumenical.
(We can't count the bullying sessions in 1225, which resulted from a cry for help against the Saracens. Rome dictated those terms as the conditions for their assistance, and then failed to send help. Thus, the other Churches quickly repudiated their submission to such Catholic doctrines as Purgatory, the Filioque, the Treasury of Merit, etc.)
We can continue to bewail the rifts in today's Church, or we can try to heal the differences that separate us. Neither is likely to do much good. Rather, we need to recognize that the Church has many functions, some of which are meant to reach the lost in ways that appeal to their individuality. The Body of Christ has many members, each with their own proper use. The Body is not all eyes, nor hands, nor so many feet, but there is a full variety and complement of organs. The truth is, we need to stop dividing over non-essential issues of doctrine and start recognizing each other as brothers and sisters in Christ. We need to "love one another" as Jesus commanded.
What we seem to lack is any means for intentional coordination, but that may not be the prerogative of any single institution of leadership. The only true head of the whole, united, catholic Church is Jesus Christ Himself, and He directs its activities by the influence of the Holy Spirit. Our opponents are the plans and institutions that work to prevent the fullness of the Kingdom of God, and seek to deceive humanity into following the broad highway of the World that leads to Hell. Let us not be distracted by our own differences, so we can focus on casting out the Enemy and his minions.
