Again, you selectively ignore certain facts.
a) The earliest churches were composed almost entirely of Jews. (There were also a few Gentiles, but very few)
Irrelevant. Had the early church been mostly composed of Chinese, it would not change Ignatius' letter.
b) You cite
one letter by Ignatius (in
English!
) and choose one word. Is that really your evidence?
It's all that is needed.
c) Again... The Coptic Church of Egypt is the earliest Christian church in the world, going back to around 42 AD. According to Bishop Eusebius of Caesarea, as well as Coptic traditions, Saint Mark the evangelist, who wrote the earliest of the four New Testament gospels, was the founder and first bishop of the Church of Alexandria, even before the Church of Rome was established. (source: ancient-origins.net)
d) "... by the end of the first century these churches were called the Catholic church". Which churches?
Yes, all these churches were connected. The oriental orthodox churches, which include the Coptic Church, didn't become independent from the Catholic Church until 451.
e) It is irrelevant if a single person wrote "wherever Jesus Christ is, there is the Catholic Church". It is a ludicrous statement. Jesus Christ is not a Catholic!!!
Of course Jesus wasn't Catholic, or any kind of Christian. Jesus was a Jew who practiced second temple Judaism. You have quite the strawman to knock down there.
There were (and are) many other Christian denominations. It is the height of arrogance to claim that the Catholic denomination is the only Christian church. There are 2,500,000,000 Christians worldwide, of which roughly half (only!) are Catholics.
This is not really the claim I was making. I think you can make a good argument that the Nazarenes (Jewish believers in Jesus in Jerusalem who continued obeying the law including sacrifices) and the churches set up by Paul were antagonistic branches. The Marcionites were similarly another branch.
What I'm claiming is that all those Gentile churches outside of Jerusalem, whether at Colossi or Ephesus or Rome or Thessalonica... were referred to as the Catholic Church by the end of the first century.
And remember, I'm NOT CATHOLIC. I'm not even a Christian. I'm a Jew. I have no dog in this race other than a truthful representation of history.