Roman Catholicism teaches that the original apostles ordained bishops as their successors and handed down the power of teaching, sanctifying, and ruling. Now, 2000 years later, they claim to have sole authority over Christ's church with their appointed bishops, the chief of which is the pope. It is important to note that Rome teaches "that the bishops have by divine institution taken the place of the apostles as pastors of the Church, in such wise that whoever listens to them is listening to Christ and whoever despises them despises Christ and him who sent Christ" (CCC 862).
This teaching is not biblical. Nowhere in God's Word is the authority of the apostles handed down to successors nor is there a supreme authority found in Peter or his supposed successors. When addressing the Corinthian church about divisions within, the apostle Paul called out the unspiritual human arguments, "I follow Paul" and "I follow Apollos" (1 Cor. 3:4). He goes on to note that within the church, it is God who provides the growth (v. 6-7), the leaders are fellow workers (v. 9) and that the foundation is Jesus Christ (v. 11). He even goes on to note that no one should boast in men, including himself, Apollos, or Peter for all things belong to God (v. 21-23).
The early Christians avoided ecclesiastical titles for those who led in the church such as archbishop, cardinal, pope, primate, metropolitan, holy father, etc. In contrast, early Christians referred to themselves as brother, beloved, fellow worker, co-laborer, slave, servant, fellow soldier, and steward. Such believers received honor through their service and work in contrast to a title or position. So what does biblical leadership look like in the church? In 1 Timothy 3 and Titus 1 we see clearly that elders and deacons are to be appointed in churches. Note however that it is their conduct in relation to the Gospel that qualifies them, not a passed down authority. For this very reason when one is out of step with the Gospel, they have no authority. A great example of this is when the apostle Paul rebuked the apostle Peter because he was not straightforward about the truth of the Gospel and stood condemned (Gal. 2:11-14).
In summary, we boldly proclaim that Christ is and always has been the only Head of His true church. Elders and deacons are appointed within the church because of their spiritual maturity in relationship to the Gospel. They carry authority, not because of their position, but from Christ and His Word as they teach and preach it.