Christ established one Church. There were NO OTHER Christian chuches at the beginning.
How many Christian congregations were there that were established by the apostles in many cities around the Roman Empire?
Catholic
Were they all defined as one catholic (universal) body of Christ?
The answer is, Yes. They were.
Is the word catholic a definition or a title?
It's a definition.
Did the Jerusalem congregation agree with all the others, and with Paul? Later on, did the church at Alexandria in Egypt agree with all doctrine taught by the church at Rome?
The answer is, No.
Did the Greek churches and Eastern churches who today call themselves by the title "Orthodox" agree in all aspects of doctrine with the church at Rome?
The answer is, no. There were disagreements which eventually led to the schism you spoke of.
Orthodox
Does the word "orthodox" not define doctrine?
The answer is Yes, it does.
Did the church that calls itself Orthodox turn the definition into a title that it calls itself by?
The answer is Yes, and the church that calls itself by the title "Catholic" did the same - they took the definition of the body of Christ/the church and its congregations (plural) as a catholic body of Christ and turned it into a title they gave themselves.
Does the Greek Church
use the definition "orthodox" to claim their theology is always orthodox wherever there is disagreement between their theology and apostolic succession claims, and that of the church that began at Rome, thinking they can do so because they took a definition (orthodox) and turned it into a title for themselves?
The answer is, Yes, they do. And the church that turned the definition of catholic into a title they adopted for themselves does the same.
Does the definition "orthodox" apply to all the theology and doctrines taught by any Christian organized body of congregations just because the organized body claims its doctrines and theology are all orthodox?
The answer is, No.
Not even if they give themselves the title "Orthodox".
Likewise for the definition "catholic" - except that no one can take away the definition from any congregation in Christ. Only Christ can take away that definition - figuratively speaking removing their lamp-stand.
Were the various congregations in the various cities of the Roman Empire not all still part of the catholic body of Christ after the schism you spoke of?
The answer is,
of course they were all still part of the one catholic (universal) body of Christ.
The same goes for after the Protestant and Reformation movements led to a schism between The Vatican's church and those who broke away from the Vatican - all of them (Greek Orthodox, Eastern Orthodox, Coptic, Messianic Jewish, Baptist, Anglican etc etc)
- all are still part of the one catholic body of Christ.
"There is one body and one Spirit, even as you are called in one hope of your calling, one Lord, one faith, one baptism, one God and Father of all, who is above all and through all and in you all." (Ephesians 4:4-6).
It is
not the church that asserts that all its doctrine
is orthodox (by adopting the title Orthodox for itself) that is "in all" who believe in Christ - it is the Holy Spirit who is in all.
It is likewise not the church that calls itself by the title Catholic that is "in all" who are part of the one catholic body of Christ - it is the Holy Spirit who is in all.
Likewise it is not the Baptist or Anglican or any other one of the thousands of names and titles that is in all of those who are part of the one catholic body of Christ - it is the Holy Spirit.
It is
not the one catholic body of Christ comprised of many churches "of whom are all things, by whom are all things, and which is above all and through all and in us all" - it is God the Father and the Holy Spirit. It is Christ Himself.
You and me and everyone else besides can argue about history all we like. It does not change the fact that all who are in Christ are part of the one body of Christ that is
defined as catholic (universal) and
not one of them can claim that all its doctrine and theology is orthodox just because they assert it is - not even the one who gave itself the title "Orthodox" (because the word is a
definition referring to doctrine and theology), and not one of them can claim that they are the only catholic body - not even the one which gave itself the title "Catholic" (because the word is a
definition referring to the universal nature of the body of Christ).
St. Ignatius of Antioch, the bishop of Antioch ordained by St. Peter, was captured by the Romans. While they were transporting him to be martyred for the faith, he wrote a letter to the Smyrnaeans around 107-110 A.D., referring to the "Catholic Church," not in such a manner as if he were coining the term, but in such a manner in which he fully expected the Smyrnaeans to understand what he was talking about.
It says in paragraph 8, "Where the bishop is present, there let the congregation gather, just as where Jesus Christ is, there is the Catholic Church."
See the entire letter here:
https://www.orderofstignatius.org/files/Letters/Ignatius_to_Smyrnaeans.pdf
The disagreements didn't create NEW churches and certainly not denominations. The disagreements were WITHIN the Catholic Church. Heresies sprung up almost from the beginning, but the Church fixed them. No one started a new church over the disagreements. That's more a Protestant thing. (Orthodox splintered, too, but retained Apostolic Succession, and, therefore, all seven Sacraments. Protestants lost Apostolic Succession and, therefore only have two Sacraments.)
I don't have the time or energy to write you a dissertation on all this. I would suggest you find a reputable college that teaches history objectively, but at this point in our country, I don't know where that would be. Marxists have taken over the educational system as well as the media and a major political party. Marxism is from Satan. Students are no longer being taught how to think. They're being indoctrinated into what to think and "how to feel about it." I'm glad I'm retired and on the way out!