Since you both like to quote Early Church Fathers, here are some quotes to help you understand their views on the authority of Bishops, the Primacy of Rome, on the Eucharist, and on Schism:
“Our Apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned, and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry."
St. Clement of Rome, Letter to the Corinthians, 44:1-2, c. AD 80
"You must follow the bishop as Jesus Christ follows the Father, and the presbytery as you would the Apostles. Reverence the deacons as you would the command of God. 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 appoints. Wherever the bishop appears, let the people be there, just as wherever Jesus Christ is, there is the Catholic Church."
St. Ignatius of Antioch, Letter to the Smyrnaeans, 8:1-2, AD 107
"The Church, having received this preaching and this faith, although she is disseminated throughout the whole world, yet guarded it, as if she occupied but one house. She likewise believes these things, just as if she had but one soul and one and the same heart and harmoniously she proclaims them and teaches them and hands them down, as if she possessed but one mouth. For, while the languages of the world are diverse, nevertheless, the authority of the Tradition is one and the same."
St. Irenaeus, Against Heresies 1, 10, 2, c. AD 190
"They abstain from the Eucharist and from prayer, because they do not confess that the Eucharist is the Flesh of our Savior Jesus Christ, Flesh which suffered for our sins and which the Father, in His goodness, raised up again."
St. Ignatius of Antioch, Letter to the Smyrnaeans, 7:1, AD 107
“We call this food Eucharist; and no one else is permitted to partake of it, except one who believes our teaching to be true and who has been washed in the washing which is for the remission of sins and for regeneration, and is thereby living as Christ has enjoined. For not as common bread nor common drink do we receive these; but since Jesus Christ our Savior was made incarnate by the word of God and had both flesh and blood for our salvation, so too, as we have been taught, the food which has been made into the Eucharist by the Eucharistic prayer set down by Him, and by the change of which our blood and flesh is nurtured, is both the flesh and the blood of that incarnated Jesus.”
St. Justin Martyr, First Apology 66, A.D. 151
“Owing to the sudden and repeated calamities and misfortunes which have befallen us, we must acknowledge that we have been somewhat tardy in turning our attention to the matters in dispute among you, beloved…Accept our counsel, and you will have nothing to regret…If anyone disobey the things which have been said by Him through us, let them know that they will involve themselves in transgression and in no small danger…You will afford us joy and gladness if, being obedient to the things which we have written through the Holy Spirit, you will root out the wicked passion of jealousy.”
St. Clement of Rome*, Letter to the Corinthians, 1: 58–59, 63, A.D. 80
“Ignatius…to the church also which holds the presidency in the place of the country of the Romans, worthy of God, worthy of honor, worthy of blessing, worthy of praise, worthy of success, worthy of sanctification, and, because you hold the presidency in love, named after Christ and named after the Father.”
St. Ignatius of Antioch, Letter to the Romans, 1:1, A.D. 110
"It is possible, then, for every Church, who may wish to know the truth, to contemplate the tradition of the Apostles which has been made known throughout the whole world. And we are in a position to enumerate those who were instituted bishops by the Apostles, and their successors to our own times…But since it would be too long to enumerate in such a volume as this the successions of all the Churches, we shall confound all those who, in whatever manner, whether through self-satisfaction or vainglory, or through blindness and wicked opinion, assemble other than where it is proper, by pointing out here the successions of the bishops of the greatest and most ancient Church known to all, founded and organized at Rome by the two most glorious Apostles, Peter and Paul, that Church which has the tradition and the faith which comes down to us after having been announced to men by the Apostles. For with this Church, because of its superior origin, all Churches must agree, that is, all the faithful in the whole world; and it is in her that the faithful everywhere have maintained the Apostolic tradition."
St. Irenaeus, Against Heresies, 3, 3, 1-2, c. AD 190 **
“The Lord says to Peter: ‘I say to you,’ He says, ‘that you are Peter, and upon this rock I will build my Church’…On him He builds the Church, and to him He gives the command to feed the sheep; and although He assigns 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?”
St. Cyprian of Carthage, The Unity of the Catholic Church, 1st edition, A.D. 251 ***
“(T)hey have not the succession of Peter, who hold not the chair of Peter, which they rend by wicked schism; and this, too, they do, wickedly denying that sins can be forgiven even in the Church, whereas it was said to Peter: “I will give unto thee the keys of the kingdom of heaven, and whatsoever thou shalt bind on earth shall be bound also in heaven, and whatsoever thou shall loose on earth shall be loosed also in heaven.” And the vessel of divine election himself said: “If ye have forgiven anything to any one, I forgive also, for what I have forgiven I have done it for your sakes in the person of Christ.”
St. Ambrose of Milan, On Penance, Book One, Ch. VII, v. 33, c. A.D. 390.
“For as many as are of God and of Jesus Christ are also with the bishop. And as many as shall, in the exercise of repentance, return into the unity of the Church, these, too, shall belong to God, that they may live according to Jesus Christ. Do not err, my brethren. If any man follows him that makes a schism in the Church, he shall not inherit the kingdom of God. If any one walks according to a strange opinion, he agrees not with the passion of Christ.”
St. Ignatius of Antioch, Letter to the Philadelphians, 3.2, ca. A.D. 110
“There is nothing more serious than the sacrilege of schism because there is no just cause for severing the unity of the Church.”
St. Augustine, Treatise On Baptism Against the Donatists, Bk 5, Ch. 1, A.D. 400
It's pointless. I quoted a few of those and they choose to ignore them. Not going to make much progress here.
But what does this prove??? How do we know this is the same Clement Paul referred to???
All we really know is that your church claims to have some letters, or copies of letters said to have been written centuries ago by 'your church fathers'...There's no proof that these letters weren't written much later by who knows who...
There are two sets of the same letters by Ignatius...One talks about the Catholic church and one doesn't...Curious, eh???
***You will also note that St. Cyprian says the “primacy is given to Peter, whereby it is made clear that there is but one Church and one chair.”
**You will note that St. Irenaeus wrote - in AD 190 - concerning “the successions of the bishops of the greatest and most ancient Church known to all, founded and organized at Rome by the two most glorious Apostles, Peter and Paul, that Church which has the tradition and the faith which comes down to us after having been announced to men by the Apostles.” So, from earliest Christianity, the Church at Rome was seen to have primacy.
You guys would be in a heap of hurt if it was proven that Peter was never in Rome...Irenaeus here seems to put Peter and Paul as equals...And since supposedly Peter and Paul were both in Rome, and Paul was the Apostle to the Gentile church, why was not Paul in the apostolic succession...He should have been the 2nd pope...And John the 3rd...What's up with that???
If you read any of the translations of St. Clements' Letter To The Corinthians you will note it is unsigned and makes no claim whatsoever to "Primacy". The letter in question, even if authentic, proves nothing.
The Ignatius leters are even more problematic with most, if not all, being proven forgeries.
I don't believe it is necessary to critique your response any further. It has already proven to be unreliable.