20 Counterarguments Against An Original Papacy:
1 The Book of Acts shows a twelve-fold collegium acting in consensus.
2 The Apostle Paul is called and ordained independently from this original apostolic collegium, denies that his authority derives from there, and claims to have a parallel vocation and authority to that of Peter (see especially Gal. 2:8).
3 The Jerusalem Council in Acts 15 shows a conciliar model of church authority with James holding the position of council president.
4 Paul selected successors directly and ordained them to ministerial positions without subordinating himself or them to any higher ecclesiastical authority (see his relationship with Timothy).
5 Bishops and elders are the same office in the New Testament, and they are local church officers (Acts 20:17; Titus 1:5, 7; 1 Peter 5:2).
6 Paul left a group of bishops in charge of the church at Ephesus (Acts 20:17, 28).
7 With the exception of the letters of Ignatius, all of the post-Biblical 1st century literature continues to use the names “bishop” and “elder” for the same office.
8 The First Epistle of Clement says that bishops are appointed “with the consent of the whole church” (1 Clement 44:2). This will later be repeated by Hippolytus of Rome (Apostolic Tradition part 1, section 2.1-5) and Cyprian (Epistle 51.8, 67.5).
9 Ignatius does speak of a bishop standing over the rest of the elders, but his bishop is still a local pastoral figure, one who is instructed to be present at baptisms and eucharists, to oversee weddings, and to know “all men by name” (Letter to Polycarp 4.2).
10 Ignatius gives some reason to think that his position on the bishop was understood as a historical innovation in his own day, and he says that he was taught his view through a charismatic revelation (Letter to the Philadelphians 7:1-2).
11 Both Ignatius and Polycarp deny that they exert the same kind of authority as the apostles (Ignatius, Letter to the Romans 4:3; Polycarp, Letter to the Philippians 3:1-2).
12 Writing around the end of the 2nd century, Irenaeus still calls “bishops” by the name of “presbyters,” though he indicates that the bishop stands over the presbyters in a leading capacity.
13 Irenaeus is the first to argue that the church of Rome was founded by Peter, but he actually argues that it was founded by both Peter and Paul (Against Heresies, 3.3.2).
14 Lists of bishops and their successors began to be written around the end of the 2nd century, but an important contradiction arises as to who Peter ordained as his immediate successor. Irenaeus states that Peter first ordained Linus as his successor and that Linus was followed by Cletus who was then followed by Clement (Against Heresies 3.3.3). Tertullian, writing not long after Irenaeus, states that Peter ordained Clement as his successor (Prescription Against Heretics 32). This gave rise to conflicting lists of bishops which Epiphanius, writing in the fourth century, harmonizes by saying that Peter ordained multiple bishops over the same churches at the same time (Panarion, Book 1, Section 2, 27.6.1-6). Thus when evidence begins to arise for a singular episcopal leader at Rome, it is soon accompanied by contradictory evidence.
15 Tertullian says that contradictory traditions should be prejudged as false (Prescription Against Heretics 21, 28). He says that the rule of faith for proving something to be “apostolic” is that it agrees with the whole church.
16 Tertullian argues that Rome has a position of primacy because Peter and Paul were martyred there (Prescription Against Heretics 36, Against Marcion 4.5). Later in Tertullian’s life, he explicitly rejected the claim that Rome inherited Peter’s apostolic power (On Modesty, chapt 21).
17 Cyprian argues that all bishops equally possess the episcopal authority of Peter (Epistle 26.1 ANF citation, Unity of the Church 4).
18 Cyprian argues that distant church courts should not overturn the judgments of local church courts (Epistle 51.14, ANF citation).
19 Cyprian argues that church-wide consent is the highest authority and that even the bishop of Rome should submit to the judgment of the whole church, which is discerned through councils (Epistle 30.1; 51.4-5, 8 ANF citation).
20 Augustine, writing about 150 years later, restates Cyprian’s position on the authority of councils and says that writing of a bishop (even the bishop of Rome) cannot require another bishop to change his practice. Only a plenary council can resolve disputes over tradition (On Baptism 2.3.4).
If you want to know how to arrive to this conclusion there are 5 articles: https://calvinistinternational.com/2018/09/19/the-leadership-of-the-catholic-church-now-vs-then-pt-6/