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The term Catholic was only beginning to be used AFTER the Scriptures had already been written. Also, when that term was used it did not refer to any one particular church, or groups of churches, it was used referring to the universal group of believers

This is that famous first usage:

Chapter 8. Let nothing be done without the bishop.
See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid.
(The Epistle of Ignatius to the Smyrnaeans)

In the same letter he also says "if they believe not in the blood of Christ, shall, in consequence, incur condemnation." Obviously, that "universal group of believers" did not contain a single Protestant.

wherever Jesus Christ is, there is the Catholic Church.

When someone has one thing right it doesn't mean he has all things right.

These early theologians were very thoughtful, but they were also products of their environment. Just as the Jews failed to see the Messiah when he stood in front of them, in part because they expected different things from their Messiah, these early theologians failed to see that our Saviour Jesus Christ not only saved all who believe The Gospel but ended the hierarchical system. Because of this in ability to see how sweeping the change was there was a strong desire to recreate the Judaic model. Which in the end is what your church did.