My knowledge of history is shabby but I was curious about this and wanted to ask… during the East-West schism with the conflict between Rome and Constantinople, if Rome was correct and if it was the primal/supremal See, then why did not any of the other sees side with Rome?
The most neutral answer one can possibly give is that there was a large cultural divide, which only continued to get wider. Any detailed answer beyond such would probably be insufficient. If you wish to look into the history of the matter, then I suggest you find a library that can get you the listed materials below. I’ve posted this list in another thread before, but I think it would helpful to you if you really want to find a satisfactory answer. Someone here as already given you the title of a great book by Francis Dvornik. I’ve listed the works below in the suggested reading order. The books and articles highlighted in blue are those that specifically concern the schism, should you choose to read only them. The others merely highlight the development of the Latin Church, which I deem equally important.
1.) Noble, Thomas F. X. “The Christian Church as an Institution.” In The Cambridge History of Christianity, 3: Early Medieval Christianities, c. 600 - c. 1100. Edited by Thomas Noble and Julia Smith. Cambridge: Cambridge University Press, 2008.
2.) Noble, Thomas F. X. “Michele Maccarrone on the Medieval Papacy.” Catholic Historical Review 80, no. 3 (1994): 518-533.
3.) Noble, Thomas F. X. “Morbidity and Vitality in the History of the Early Medieval Papacy.” The Catholic Historical Review 81, no. 4 (Oct. 1995), 505-540.
4.) Noble, Thomas F. X. The Republic of St. Peter: The Birth of the Papal State, 680-825. Philadelphia: University of Pennsylvania Press, 1984.
5.) Dvornik, Francis. Byzantium and the Roman Primacy. New York: Fordham University Press, 1966. Corrected edition, 1979.
6.) Gallagher, Clarence. “Diversity in Unity: Approaches to Church Order in Rome and Byzantium.” Ecclesiastical Law Journal: The Journal of the Ecclesiastical Law Society 6, no. 30 (2002): 208-238.
7.) Herrin, Judith. “The Pentarchy: Theory and Reality in the Ninth Century.” In Cristianità d’Occidente e cristianità d’Oriente (secoli VI-XI) : 24-30 aprile 2003. Spoleto, Italy: Settimane di studio della Fondazione Centro italiano di studi sull’Alto Medioevo, 2004. 591-628.
8.) Noble, Thomas F. X. “The Intellectual Culture of the Early Medieval Papacy.” Roma nell’Alto Medioevo, 27 aprile - 1 maggio 2000. Spoleto, Italy: Settimane di studio della Fondazione Centro italiano di studi sull’Alto Medioevo, 48. 2001. 179-213.
9.) Meyendorff, John. Imperial Unity and Christian Division: The Church, 450-680 A.D. Crestwood, NY: St. Valdimir’s Seminary Press, 1992.
10.) Runciman, Steven. The Eastern Schism: A Study of the Papacy and the Eastern Churches during the XIth and XIIth Cenuturies. Oxford: Clarendon Press, 1955.
11.) Grant, Ken. “A Divine Mandate: Pope Gregory VII’s Defense of Papal Authority.” In Authorities in the Middle Ages: Influence, Legitimacy, and Power in Medieval Society. Edited by Sini Kangas et al. 2013. 39-54. ISBN 978-3-11-029449-1
12.) Eldevik, John. Episcopal Power and Ecclesiastical Reform in the German Empire: Tithes, Lordship, and Community, 950-1150. New York: Cambridge University Press, 2012.
I realize this is a lot, but considering that your question is not a small one, it does not hurt to be too informed. Most of these works, of course, cover the Middle Ages. I do not know the religious affiliation of Thomas Noble, Judith Herrin, Clarence Gallagher, Ken Grant, Steven Runciman, or John Eldevik. They seem to keep such personal matters out of their work. Gallagher though is a theologian of some sort I imagine. Francis Dvornik was a Catholic priest. His work is good, but it is clear that he does have an agenda. John Meyendorff was an Orthodox theologian, who wrote a lot on church history and patristics. I picked his book precisely because Thomas Noble said it was good and recommended it in one of his footnotes.
Steven Runciman is dead, but he was a highly respected Mediterranean historian for his time. Thomas Noble is a Carolingian historian who tends to focus on papal Rome during the Early Middle Ages. Judith Herrin is now retired, but she is probably one of the most respected Byzantine historians in the field right now. Ken Grant and John Eldevik are historians. I can testify to the quality of John Eldevik’s work, but it is daunting despite its relatively short length.
I’ve listed these in the order I think you should read them. #1 is fairly easy to read. #2 is essentially a book review and summary of a history that is written only in Italian sadly. #3 is the most important thing to read before going any further down the list. You must not skip it. Although it is 20 years old, Noble gives you a basic summary of all the historical work regarding the papacy. His concerns about it, and vision for expanding the work are very much applicable to this day. It will help you understand the rest of what you read. John Eldevik’s book will be the most difficult for you to read probably, which is why it is last. It also covers the latest time frame on this list. All the books and articles here basically cover the fourth century AD to 1200 AD. I focused on this period, because sadly we have very few sources that can illuminate much on the Roman primacy. They can be interpreted either way because they are so vague. The Late Antique Period, the Early Middle Ages, and the High Middle Ages are the places where you are most likely to find your answer.
P.S. Despite some of these works being in foreign language essay collections, all of them are written in English.