To be Catholic...

We profess to believe in a Church, an assembly of believers, that is catholic. While there is a nominal value to the big-C title, Roman Catholic, the adjective catholic was always used to identify the Church as manifesting particular properties that distinguished it from the myriad of heretical sects that have abounded through history. The Church is catholic, meaning it is universally apparent and one in unity of doctrine. It is also visible and organized, as attested to by St. Ignatius of Antioch in his letter to the Church at Smyrna, written approx. 110 AD:

Let no one do anything of concern to the Church without the bishop. Let that be considered a valid Eucharist which is celebrated by the bishop or by one whom he ordains [i.e., a presbyter]. Wherever the bishop appears, let the people be there; just as wherever Jesus Christ is, there is the Catholic Church.

This makes the term peculiar to one assembly of believers throughout the world where the teaching of Christ can be found, sent out by Christ on a mission to the entire world.

St. Cyril of Jerusalem, in paragraphs 22-28 of his 18th catechetical lecture, written approx. 350 AD, wrote intensely about what is meant when we profess that we believe in the Catholic Church.

[The Church (Greek "ecclesia" = assembly)] is called Catholic [(Greek "katholicos" = universal)] then because it extends over all the world, from one end of the earth to the other; and because it teaches universally and completely one and all the doctrines which ought to come to men's knowledge, concerning things both visible and invisible, heavenly and earthly; and because it brings into subjection to godliness the whole race of mankind, governors and governed, learned and unlearned; and because it universally treats and heals the whole class of sins, which are committed by soul or body, and possesses in itself every form of virtue which is named, both in deeds and words, and in every kind of spiritual gifts.

Based on this, St. Cyril went on to give an important admonition:

And if ever thou art sojourning in cities, inquire not simply where the Lord's House is (for the other sects of the profane also attempt to call their own dens "houses of the Lord"), nor merely where the Church is, but where is the Catholic Church. For this is the peculiar name of this Holy Church, the mother of us all, which is the spouse of our Lord Jesus Christ, the Only-begotten Son of God...

In this Holy Catholic Church receiving instruction and behaving ourselves virtuously, we shall attain the kingdom of heaven, and inherit Eternal Life; for which also we endure all toils, that we may be made partakers thereof from the Lord.

It is the peculiar Church that is Catholic, and at the same time, it is also One, Holy, and Apostolic. The mother of us all. Protected by Christ in spite of the sinfulness of its members in view of the merits of His death and resurrection.