..... we consider our Church to be the only one that preserved the apostolic teachings and the pontifex of Rome splitted his part of the Church from the rest etc...
As you well know every church will try to say that it is the original and true Church established by Christ. I would not be surprised if many of the Protestant churches claim that same thing. Should we believe them all?
It is obvious that Christ instituted one Church only: And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it.
Christ was speaking singly (thee in the original languages was for a single person) to Peter and no one else. Note that Christ says "My Church" which means it is one church (not churches) and it belongs to Christ.
So it is either we are the one or one of the Orthodox churches is the one. We cannot be both the one. Which one is it?
Let us see what the Fathers of the Church (which we both believe in) have to say:
"The Lord says to Peter: ‘I say to you,’ he says, ‘that you are Peter, and upon this rock I will build my Church, and the gates of hell will not overcome it. ... ’ [Matt. 16:18]. On him [Peter] he builds the Church, and to him he gives the command to feed the sheep [John 21:17], and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. . . . If someone [today] does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?"
Cyprian of Carthage (The Unity of the Catholic Church 4; first edition [A.D. 251]).
"To be in communion with Cornelius is to be in communion with the Catholic Church" (St. Cyprian: Ep. Iv., n. 1). Cornelius was Pope of Rome
"Heresies and schisms have no other origin than that obedience is refused to the priest of God, and that men lose sight of the fact that there is one judge in the place of Christ in this world" St. Cyprian (Epist. xii. ad Cornelium, n. 5).
But if you are near Italy, you have Rome, where authority is at hand for us too. Tertullian, Demurrer Against the Heretics 36 and 32:2,
"The Son committed to Peter the office of spreading the knowledge of His Father and Himself over the whole world. He who increased the Church in all the earth, and proclaimed it to be stronger than the heavens, gave to a mortal man all power in Heaven when He handed him the Keys"
St. John Chrysostom Bishop of Constantinople, Hom. Liv, in Matt. v., 2.
"Why has He shed His blood? To buy the sheep which He handed over to Peter and his successors" St. John Chrysostom, De Sacerdotio, lib. ii.
Referring to the Church in Rome : "With this Church, on account of its preeminent authority,, it is necessary that every Church should be in concord"
St. Irenaeus, Contra Haereses, lib. iii., cap. 3, n. 2
"The primacy of the Apostolic chair always existed in the Roman Church " St. Augustine, Ep. xliii., n. 7
Referring to the see of Rome "the Apostolic See has received and hath government, authority, and power of binding and loosing from the Incarnate Word Himself; and, according to all holy synods, sacred canons and decrees, in all things and through all things, in respect of all the holy churches of God throughout the whole world, since the Word in Heaven who rules the Heavenly powers binds and loosens there"
Maximus the Abbot, Defloratio ex Epistola ad Petrum illustrem.
"You cannot deny that you know that in the city of Rome the Episcopal chair was first conferred on Peter. In this Peter, the head of all the Apostles (hence his name Cephas), has sat; in which chair alone unity was to be preserved for all, lest any of the other apostles should claim anything as exclusively his own. So much so, that he who would place another chair against that one chair, would be a schismatic and a sinner" Optatus of Milevis, De Schism. Donat., lib. ii.
"Against which ages (of hell) we read that Peter received the saving keys, that is to say, our prince, to whom it was said by Christ: 'To thee will I give the keys of the Kingdom of Heaven, and the gates of hell shall not conquer them.' Whence is it therefore that you strive to obtain for yourselves the keys of the Kingdom of Heaven—you who fight against the chair of Peter?" Optatus of Milevis, Lib. ii., n. 4-5.
"It is evident to all who know the gospel that the charge of the whole Church was committed to St. Peter, the Apostle and Prince of all tie Apostles, by the word of the Lord....Behold! he hath received the keys of the heavenly kingdom—the power of binding and loosing is conferred upon him: the care of the whole government of the Church is confided to him " St. Gregory the Great, Epist. Iib. v., Epist. xx.
“Christ is the light and the lampstand is Peter; the oil, however, is the activity of the Holy Spirit. Hail, O Peter, gate of sinners, tongue of the disciples, voice of preachers, eye of the Apostles, guardian of heaven, the first-born of the keepers of the keys.” St. Ephrem the Syrian, Encom. in Petrum et Paulum
“Simon, my disciple, I have made you the foundation of the holy Church. I called you "rock" that you might sustain my entire building. You are the overseer of those who build a church for me on earth. If they should wish to build something forbidden, prevent them, for you are the foundation. You are the head of the fountain from which my doctrine is drawn. You are the head of my disciples. Through you all nations shall drink. Yours is that vivifying sweetness that I bestow. I have chosen you to be as a firstborn in my institution and heir to all my treasures. The keys of the kingdom I have given to you, and behold I make you prince over all my treasures. ” St. Ephrem the Syrian, Lamy, S. Ephr. Hymn. et Serm., vol. 1, pr. 411
“The extremities of the earth, and all in every part of it who purely and rightly confess the Lord look directly towards the most holy Roman Church and its confession and faith, as it were to a sun of unfailing light, awaiting from it the bright radiance of the sacred dogmas of our Fathers according to what the six inspired and holy councils have purely and piously decreed, declaring most expressly the symbol of faith.For from the coming down of the incarnate Word amongst us, all the Churches in every part of the world have held that greatest Church alone as their base and foundation, seeing that according to the promise of Christ our Saviour, the gates of hell do never prevail against it, that it has the keys of a right confession and faith in Him, that it opens the true and only religion to such as approach with piety, and shuts up and locks every heretical mouth that speaks injustice against the Most High.” St. Maximus the Confessor (St. Maximus of Constantinople)
"This most holy See has preserved the supremacy over all Churches on the earth, for one especial reason among many others; to wit, that it has remained intact from the defilement of heresy. No one has ever sat on that Chair, who has taught heretical doctrine; rather that See has ever preserved unstained the Apostolic grace." Theodoret of Cyr (Epistle 116 to Renatus).
"The Lord said to Peter, ‘On this rock I will build my Church, I have given you the keys of the kingdom of heaven [and] whatever you shall have bound or loosed on earth will be bound or loosed in heaven’ Matt. 16:18–1. . . Upon you, he says, I will build my Church; and I will give to you the keys, not to the Church; and whatever you shall have bound or you shall have loosed, not what they shall have bound or they shall have loosed" Tertullian (Modesty 21:9–10 [A.D. 220]).
"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 (Peter) he builds the Church, and to him he gives the command to feed the sheep (John 21:17), and although he assigns a like power to all the apostles, yet he founded a single chair (cathedra), 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 (i.e., apostles), but a primacy is given to Peter, whereby it is made clear that there is but one Church and one chair. So too, all (the apostles) 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 (should) desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?"
Cyprian of Carthage -The Unity of the Catholic Church 4; 1st edition (A.D. 251).
"But that great man, the disciple of disciples, that master among masters, who wielding the government of the Roman Church possessed the authority in faith and priesthood. Tell us therefore, tell us we beg of you, Peter, prince of the Apostles, tell us how the churches must believe in God."Cassian John,Contra Nestorium,3:12(A.D. 430),in SPP,61
"The decrees of the Roman Pontiff, standing upon the supremacy of the Apostolic See, are unquestionable."
Isidore of Seville,(ante A.D. 636),in PL:84
"But since the word Ecclesia is applied to different things...., and since one might properly and truly say that there is a Church of evil doers, I mean the meetings of the heretics, the Marcionists and Manichees, and the rest, for this cause the Faith has securely delivered to thee now the Article, "And in one Holy Catholic Church;" that thou mayest avoid their wretched meetings, and ever abide with the Holy Church Catholic in which thou wast regenerated. 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 (for it is written, As Christ also loved the Church and gave Himself for it, and all the rest,) and is a figure and copy of Jerusalem which is above, which is free, and the mother of us all; which before was barren, but now has many children.” St. Cyril of Jerusalem, lecture XVIII
"And last, the very name Catholic, which, not without reason, belongs to this Church alone, in the face of so many heretics, so much so that, although all heretics want to be called ‘Catholic,’ when a stranger inquires where the Catholic Church meets, none of the heretics would dare to point out his own basilica or house"
St. Augustine (Against the Letter of Mani Called "The Foundation" 4:5 [A.D. 397]).
"You are not to be looked upon as holding the true Catholic faith if you do not teach that the faith of Rome is to be held " (St. Augustine, Sermo cxx., n. 13).
"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"
Peter Chrysologus(Letters 25:2 [A.D. 449]).
Let us also see what the early councils had to say:
Of the care and power which a Patriarch has over the bishops and archbishops of his patriarchate; and of the primacy of the Bishop of Rome over all.
Let the patriarch consider what things are done by the archbishops and bishops in their provinces; and if he shall find anything done by them otherwise than it should be, let him change it, and order it, as seemeth him fit: for he is the father of all, and they are his sons. And although the archbishop be among the bishops as an elder brother, who hath the care of his brethren, and to whom they owe obedience because he is over them; yet the patriarch is to all those who are under his power, just as he who holds the seat of Rome, is the head and prince of all patriarchs; inasmuch as he is first, as was Peter, to whom power is given over all Christian princes, and over all their peoples, as he who is the Vicar of Christ our Lord over all peoples and over the whole Christian Church, and whoever shall contradict this, is excommunicated by the Synod” The First Council of Nicea-The Arabic Canons
"Philip, presbyter and legate of (Pope Celestine I) said: ‘We offer our thanks to the holy and venerable synod, that when the writings of our holy and blessed pope had been read to you . . . you joined yourselves to the holy head also by your holy acclamations. For your blessednesses is not ignorant that the head of the whole faith, the head of the apostles, is blessed Peter the apostle’" Council of Ephesus(Acts of the Council, session 2 [A.D. 431]).
"A copy of the letter sent by the holy and Ecumenical Sixth Council to Agatho, the most blessed and most holy pope of Old Rome...Serious illnesses call for greater helps, as you know, most blessed (father); and therefore Christ our true God, who is the creator and governing power of all things, gave a wise physician, namely your God-honoured sanctity, to drive away by force the contagion of heretical pestilence by the remedies of orthodoxy, and to give the strength of health to the members of the church. Therefore to thee, as to the bishop of the first see of the Universal Church, we leave what must be done, since you willingly take for your standing ground the firm rock of the faith, as we know from having read your true confession in the letter sent by your fatherly beatitude to the most pious emperor: and we acknowledge that this letter was divinely written (perscriptas) as by the Chief of the Apostles, and through it we have cast out the heretical sect of many errors which had recently sprung up.."Constantinople III Council to Pope Agatho,(A.D. 680),NPNF2,XIV:349
"Wherefore the most holy and blessed Leo, archbishop of the great and elder Rome, through us, and through this present most holy synod together with the thrice blessed and all-glorious Peter the Apostle, who is the rock and foundation of the Catholic Church, and the foundation of the orthodox faith..."Council of Chalcedon,Session III (A.D. 451),in NPNF2,XIV:259-260
"There is no doubt, and in fact it has been known in all ages, that the holy and most blessed Peter, prince and head of the Apostles, pillar of faith, and foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Savior and Redeemer of the human race, and that to him was given the power of loosing and binding sins: who down even to to-day and forever, lives and judges in his successors. The holy and most blessed Pope Celestine,according to due order,is his successor and holds his place..."
Philip,Council of Ephesus,Session III (A.D. 431),in NPNF,XIV:223
If you can show me the same type of quotes of the Fathers and of councils, applied to any other church besides that of Rome (eg church of Constantinople or Church of Antioch etc...) or to any other Apostle besides St Peter (eg St John or St Matthew) then we can both agree that the see of Peter is equivalent to all the other sees and that the Church of Rome is also equivalent to all the other churches.
If you cannot find these quotes and if you want to follow the Fathers then you have to accept what they are saying here about the See of Rome and the Chair of Peter.