Catholics were not the Authors of any scripture.
Matthew, Mark, Luke, and John were followers of Jesus Christ. Followers of Christ might not have not been called Christians when they started following Him, but they were Christians in every sense of the word. Christian/Catholic, one in the same. There was only one type of Christian/Catholic back then. There were no protestants. Sorry to disappoint you.
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I don’t know what you are referring to when you talk about Protestants being around back then, I suppose you have my words confused with someone else’s words.
By the time the word “Christian” started being used likely all the scripture we have today was written.
Followers of Christ were called “Christians” very shortly after the death of the Apostles. The need for written words of the Apostles arose because they died off and the people that had heard them in life were beginning to die off too. Nobody in the early church suspected the world to continue so long, they expected the second coming to be in their lifetimes, perhaps every generation does. Anyway since the Apostles and those that heard them in life were no longer around their words needed to be written. Memories of the sermons of the Apostles are what we have in the Gospels.
Christian and Catholic are not the same thing. Christians are followers of Christ or members of a church that Teach Christ. Catholic simply means Universal. The Church was not “Universal” at least until after 325 some will say sometimes in the 380’s that the term “Universal” was first used. Whenever it was used it started becoming universal after the first council of Nicea in 325.
Protestants broke away from the Christian Church 500 years ago. Does the name Martin Luther ring a bell? They are ecclesial communities, they are not churches. There is no apostolic succession in any faith born out of the Reformation.