The Catholic Church includes all of the local (particular) churches in full communion with the Bishop of Rome, who is the successor of St. Peter. It was St. Peter who was entrusted by the Lord Jesus Christ as the shepherd to stand in the place of the Good Shepherd (John 10:11) and feed His sheep (John 21:15).
This is the case today, and has been the case since the first century.
However, Protestants will give various arguments to justify their separation from Rome. These are usually lacking in historical context or knowledge about the history of the Christian movement.
The Gospel of Matthew is clear enough, and later Christians were aware of these words and Peter's ministry and martyrdom in Rome:
Jesus instructed His followers to build on rock for a solid foundation (Matthew 7:24). Then He takes one apostle named Simon and gives him the new name of Rock! (Matthew 16:18) On this Rock, He will build His Church. How much clearer can that be? Peter means Rock and Peter is always known after this as Rock and not Simon any longer.
So, let's look at some quotes from the Christian leaders of the early Church, did Rome have a special status or not?
Before the first century even ended, while the apostle John was living, the Church of Rome made a powerful intervention in the affairs of the church at Corinth!
IN THE FIRST CENTURY (96 AD, Epistle of Clement to Corinth, chapter 59):
"If, however, any shall disobey the words spoken by Him through us, let them know that they will involve themselves in transgression and serious danger"
Does that sound like none of the churches had any authority over the others? Don't forget, St. Peter himself actually taught the Christian faith to this man!
180 AD: Less than a century after the apostolic age ended around 100 AD (St. Irenaeus, Against Heresies)
Speaking of the Church of Rome: "it is a matter of necessity that every Church should agree with this Church, on account of its preeminent authority"
Don't forget, St. Irenaeus learned the Christian faith from St. Polycarp who was a disciple of St. John the apostle.
Clement of Alexandria says in 200 AD:
“[T]he blessed Peter, the chosen, the preeminent, the first among the disciples, for whom alone with himself the Savior paid the tribute [Matt. 17:27],
Let's move on to 251 AD, in North Africa with St. Cyprian:
"[After quoting Matthew 16:18f; John 21:15ff]...On him [Peter] He builds the Church, and to him He gives the command to feed the sheep; and although He assigned a like power to all the Apostles, yet he founded a single Chair, and He established by His own authority a source and an intrinsic reason for that unity. Indeed, the others were that also which Peter was; but a primacy is given to Peter, whereby it is made clear that there is but one Church and one Chair. So too, all are shepherds, and the flock is shown to be one, fed by all the Apostles in single-minded accord. If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?" (Cyprian, The Unity of the Catholic Church [first edition] 4, c. AD 251)
"They who have not peace themselves now offer peace to others. They who have withdrawn from the Church promise to lead back and to recall the lapsed to the Church. There is one God and one Christ, and one Church, and one Chair founded on Peter by the word of the Lord. It is not possible to set up another altar or for there to be another priesthood besides that one altar and that one priesthood. Whoever has gathered elsewehre is scattering." (Cyprian, Letter 43 (40), 5, c. AD 251)
"With a false bishop appointed for themselves by heretics, they dare even to set sail and carry letters from schismatics and blasphemers to the chair of Peter and to the principal Church [at Rome], in which sacerdotal unity has its source; (Cyprian, Letter 59 (55), 14 to Cornelius of Rome, c. AD 252)
Now, at this point, remember we are still at a time when the Christian faith was illegal, under persecution, before the council of Nicea, and over a century before the canon of Scripture would be set by councils.
That's right, the primacy of Peter and Rome in the early Church is established well before the canon of the New Testament.
How about a famous saint, St. Jerome, in 367 AD, writing to Pope Damascus, still before the canon was established:
it is but with the successor of the fisherman and the disciple of the Cross that I speak. Following none in the first place but Christ, I am in communion with your beatitude, that is, with the Chair of Peter. On that rock I know the Church is built. Whosoever shall eat the Lamb outside that house if profane. If any be not with Noah in the Ark, he shall perish beneath the sway of the deluge.
How about an even more famous saint, St. Augustine:
“There are many other things which rightly keep me in the bosom of the Catholic Church. The consent of the people and nations keeps me, her authority keeps me, inaugurated by miracles, nourished in hope, enlarged by love, and established by age. The succession of priests keep me, from the very seat of the apostle Peter (to whom the Lord after his resurrection gave charge to feed his sheep) down to the present episcopate [of Pope Siricius]” -Saint Augustine, Father and Doctor of the Church, Against the Letter of Mani Called “The Foundation” 5 [A.D. 397].
Yet another, St. John Chrysostom, Patriarch of Constantinople, 387 AD:
(Peter), the foundation of the Church, the Coryphaeus of the choir of the Apostles, the vehement lover of Christ ...he who ran throughout the whole world, who fished the whole world; this holy Coryphaeus of the blessed choir; the ardent disciple, who was entrusted with the keys of heaven, who received the spiritual revelation. Peter, the mouth of all Apostles, the head of that company, the ruler of the whole world. (De Eleemos, iii. 4; Hom. de decem mille tal. 3)
In those days Peter rose up in the midst of the disciples (Acts 15), both as being ardent, and as entrusted by Christ with the flock ...he first acts with authority in the matter, as having all put into his hands ; for to him Christ said, 'And thou, being converted, confirm thy brethren. (Chrysostom, Hom. iii Act Apost. tom. ix.)
St. Athanasius (362), the great defender of orthodoxy:
Rome is called the Apostolic throne. (Athanasius, Hist. Arian, ad Monach. n. 35)
The Chief, Peter. (Athan, In Ps. xv. 8, tom. iii. p. 106, Migne)
Saint Peter Chrysologus, Father and Doctor of the Church (Letters 25:2 [A.D. 449]:
“We exhort you in every respect, honorable brother, to heed obediently what has been written by the most blessed pope of the city of Rome, for blessed Peter, who lives and presides in his own see, provides the truth of faith to those who seek it. For we, by reason of our pursuit of peace and faith, cannot try cases on the faith without the consent of the bishop of Rome”
Is that enough yet? There are dozens more if you want to look at www.fisheaters.com
Case closed. As St. Augustine said, "Rome has spoken; the case is closed" (from his Sermons 131:10).
For more early Church insight that Protestants need to learn, read on - Top 5 Early Church Quotes That Protestants Don't Know