One of the main arguments that the RCC has for the primacy or the overall leadership bestowed on the Roman Pope is the historical term used that the Roman Bishop is “the first among equals”. Per the following website article, https://graceuniversity.edu/iip/2011/08/11-08-20-1/
“Organizationally, the church developed from a plurality of church leadership in the 1st century (e.g., Philippians 1:1), to a bishop having authority over several churches in the 2nd century, to a hierarchical structure into 3rd and 4th centuries. By the 5th century, the church regarded the Bishop of Rome as the first among equals and the city of Rome as its geographical center. Through church councils (e.g., Nicea  and Chalcedon  and others), the church reached agreement that the Bible taught God is Trinity, Jesus is God, His death is a substitutionary one and that He is coming again. Protestant church historians generally maintain that institutionalized Roman Catholicism began with Gregory’s appointment as bishop of Rome in A.D. 590. Though he refused the title pope, administratively, he organized the papal system of government that characterized the entire medieval period. “
The other 4 key regional bishops, or Patriarchs, considered that giving Rome the title “First among Equals” was merely honorary and symbolic- and that it did not give the Roman Bishop any additional powers or obligation or influence. Rome, of course, did not see it that way. The Roman Empire was defeated and ended in 476 AD, and following that point it is clear that the Roman Bishop of the Church wanted to maintain a high degree of influence in the known world. This disagreement led eventually to the Great Schism of 1054 AD, where the West (the RCC) split from the Orthodox Church (in the Eastern part of the former Roman Empire). One quick anecdote: What is the true meaning of being “first, among equals”? Does that phrase mean that the first is the “best”, or “most important”, or “most powerful” ?
If we think about the United States, Delaware is historically known as “The First State”. It is on their license plates to this day. Delaware is a State, just like the other equivalent 49 States. Because Delaware was first, is it the best State? The most important or powerful? Not hardly- and that takes nothing away from the people in Delaware. The point is- the old title in the Church can be seen as semantics, and an argument can be made on each side. And, it was made.