St. Cyril of Jerusalem - Why the Catholic Church IS the Church Founded By Jesus

From the Jerusalem Catecheses by St Cyril of Jerusalem (Doctor of the Church), #18
22. The Faith which we rehearse contains in order the following, And in one Baptism of repentance for the remission of sins; and in one Holy Catholic Church; and in the resurrection of the flesh; and in eternal life. Now of Baptism and repentance I have spoken in the earliest Lectures; and my present remarks concerning the resurrection of the dead have been made with reference to the Article In the resurrection of the flesh. Now then let me finish what still remains to be said for the Article, In one Holy Catholic Church, on which, though one might say many things, we will speak but briefly.
23. It is called Catholic 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.
24. And it is rightly named (Ecclesia) because it calls forth and assembles together all men; according as the Lord says in Leviticus, And make an assembly for all the congregation at the door of the tabernacle of witness. And it is to be noted, that the word assemble, is used for the first time in the Scriptures here, at the time when the Lord puts Aaron into the High-priesthood. And in Deuteronomy also the Lord says to Moses, Assemble the people unto Me, and let them hear My words, that they may learn to fear Me. Deuteronomy 4:10 And he again mentions the name of the Church, when he says concerning the Tables, And on them were written all the words which the Lord spoke with you in the mount out of the midst of the fire in the day of the Assembly ; as if he had said more plainly, in the day in which you were called and gathered together by God. The Psalmist also says, I will give thanks unto You, O Lord, in the great Congregation; I will praise You among much people.
25. Of old the Psalmist sang, Bless ye God in the congregations, even the Lord, (ye that are) from the fountains of Israel. But after the Jews for the plots which they made against the Saviour were cast away from His grace, the Saviour built out of the Gentiles a second Holy Church, the Church of us Christians, concerning which he said to Peter, And upon this rock I will build My Church, and the gates of hell shall not prevail against it. Matthew 16:18 And David prophesying of both these, said plainly of the first which was rejected, I have hated the Congregation of evil doers ; but of the second which is built up he says in the same Psalm, Lord, I have loved the beauty of Your house ; and immediately afterwards, In the Congregations will I bless you, O Lord. For now that the one Church in Judæa is cast off, the Churches of Christ are increased over all the world; and of them it is said in the Psalms, Sing unto the Lord a new song, His praise in the Congregation of Saints. Agreeably to which the prophet also said to the Jews, I have no pleasure in you, says the Lord Almighty Malachi 1:10; and immediately afterwards, For from the rising of the sun even unto the going down of the same, My name is glorified among the Gentiles. Concerning this Holy Catholic Church Paul writes to Timothy, That you may know how you ought to behave yourself in the House of God, which is the Church of the Living God, the pillar and ground of the truth 1 Timothy 3:15 .