You've been reading too much Catholic apologetics from Catholic Answers and the apologetics machinery of EWTN and Catholic radio.
Read "The Primacy of Peter" by Father John Meyendorff. I double dare ya. Read it. I would defy you to refute his historical, biblical, and patristic points that flat out blow away the Catholic views of the papacy.
There are arguments that can be made against Orthodoxy's not being a part of Catholicism, but the arguments you make here are just plain BAD ones. There was a pentarchy. Five patriarchs united as One Church. They didn't rebel and break off, as you put it, from the Pope. The Pope's clan broke off from Holy Orthodoxy. And since then have descended into an abyss of sex scandal, corruption, theological messes that look NOTHING like the ancient church, and finally awfully disgraceful Protestant-like liturgical abuse to the point that the Catholic Mass looks practically nothing like the ancient Western rites.
The Pentarchy didn't break off. Rome did. We didn't march into your cathedrals and throw down excommunication bullas. That was the West. We didn't try to unilaterally alter the Creed after previously saying we wouldn't do so. We didn't Judaize our Eucharist and take the leaven out of it and go back steps in the wrong direction. We didn't allow Charlemagne and his goons to intimidate us into the filioque position. Carolinians didn't force our hands. The Pentarchy continued well after the papacy and the West broke off. They continued the ancient polity, ancient theology, ancient liturgy, and the correct Orthodox teachings that thrive today.
Meanwhile Catholicism fell into its errors living in a vacuum.
You are living in a world of soundbites. You get on Catholic websites, receive your marching orders from some out-of-context quotes, mix them with some arguments given you by Scott Hahn and Steven Ray and the apologetics powers that be, and you don't read the entire works from which these quotes came. That's a huge problem.
The Ancient Church didn't function with this "supreme pontiff" lording over the entire Church. It just didn't work that way. You need to understand a primacy of honor, the reality that primacy doesn't equate to exclusivity or supremacy or infallibility or universal dictatorship. Doesn't work that way. Christianity WAS AND IS messy! The Councils (none of which the popes attended btw!) were messy! There was fighting, arguing, serious theological disagreement, and eventually prayer, consensus, and rich theology given. There were plenty of times the Church either flat out ignored the teachings or platitudes of the popes and other times they all-out disagreed with them and went against them. St. John Chrysostom, our Father Among the Saints, spent most of his blessed life out of communion with the Pope.
The Church allowed appeals. When clergy felt they were wrongly-treated or misjudged by their synods, they were allowed to appeal that decision before other jurisdictions. If a bishop under the Patriarch of Antioch felt he was wrongly deposed or judged, he could go to the Patriarch of Constantinople or the Patriarch of Jerusalem or the Patriarch of Antioch or the Patriarch of Rome, on and on. Many appealed to Constantinople, many to Rome, many to the others. The Bishop of Rome held great esteem (as he should!). Not only was Peter martyred in Rome, but also Paul! It was the old capital of the Empire, and great wealth and power existed in that See. Rome was right on many things. The Popes DID regularly make the right calls and fall on the right side of history. Pope St. Gregory, Pope St. Leo the Great, there were great men in Rome. Clement, on and on....
Keep in mind how many times Rome has used forgeries and false texts to "prooftext" their anachronistic claims. The Florilogia comes to mind along with the "Donation of Constantine!"
We have to look at things holistically. Between the many times that popes were ignored, the times we see a pope actually encourage a heresy (Pope Honorius not only WROTE his private heretical teachings to Sergius, he also sent his deacon Gaius to the Synod of Cyprus to ADVOCATE for monothelitism according to St. Maximos!), and the way things played out in the "Photian Schism" along with many great saints like St. John Chrysostom who lived for most if not all of their lives outside of communion with Rome coupled with the reality that men like St. Cyprian were willing to take on the popes while remembering that the Schism originated NOT in the East but in the West, there is no argument hardly at all that holds water.
Rome left Holy Orthodoxy. The tree's fruits are quite evident in 2014. Watered-down happy-clappy modernist liturgy, scandal, bad theology (infallibility, indulgences, purgatory, pandering to Islam and seeing Islam as the first saved after Catholics, poor Mariology, legalistic mindsets) it all shows nothing in common with Orthodoxy.
The Schism wasn't political, it was theological. Still is. And you guys are still dead wrong.
THANKS BE TO GOD FOR ST. MARK OF EPHESUS!
1)The Pope derives his authority from the primacy of Peter since the early years of the church the Bishop of Rome held primacy and was the leader of the Christian World.
2) No the Orthodox Changed her position for political and temporal reasons. Therefore they rebelled against the Church.
3) apostolic succession is a huge part of both of our churches