Did St. Peter view his authority as equal to other Church leaders?

Full Question
How can you say Peter had authority over other church leaders when he referred to himself as only their “fellow elder”(1 Pt 5:1). This proves Peter did not see himself as having any “primacy” in the Church. He was just a presbyter.
Answer
No, it doesn’t. To assert that Peter had no primacy is to ignore the clear passages to the contrary, such as Matthew 16:18-19, Luke 22:33, John 21:15-17, and Galatians 1:18. The answer to your question is found within the very context you cite. Peter says, “Clothe yourselves in humility in your dealings with one another, for God opposes the proud but bestows favor on the humble. So humble yourselves under the mighty hand of God, that he may exalt you in due time” (1 Pt 5:5).
By humbly calling himself a “fellow elder” Peter was not implying he was merely equal in authority to the presbyters of the Church; rather, he was practicing something he enjoined on others. This self-effacement is the virtue of humility which Jesus calls all Christians to cultivate: “Whoever wishes to be great among you shall be your servant, whoever wishes to be first among you shall be your slave” (Mt 20:26-27).
Peter elsewhere reminds his readers that he is an “apostle of Jesus Christ” and as such had authority to preach and teach in the name of the Lord (cf. Lk 10:16). The very facts that Peter sent his epistles to instruct and guide the Church, and that the Church revered them as inspired, inerrant Scripture is sufficient testimony that Peter possessed an authority above that of a presbyter.
This sort of humility in dealing with the Church is evident throughout the apostolic writings. The lowest level of priestly minister was the deacon. The apostles ordained men to this office originally to distribute food to the needy and to wait on tables (Acts 6:1-6). Yet Paul, the great and eloquent writer of about half of the New Testament, describes himself as a mere deacon on several occasions (1 Cor 3:5, 4:1; 2 Cor 3:6, 6:4, 11:23; Eph 3:7; Col 1:23, 25).
If you’re going to be consistent in claiming that Peter had no special authority above that of a presbyter, you’ll be forced to conclude that Paul was only a deacon and therefore had no authority over bishops, priests, or other deacons. But nobody would make such a patently unbiblical assertion.
Paul, like Peter, presents himself in a humble, unassuming way–“I am the least of the apostles, not fit to be called an apostle, because I persecuted the church of God” (1 Cor 15:10), “To me the very least of all the holy ones, this grace was given” (Eph 3:8)–but such humility does not indicate that Paul did not have jurisdiction over others. After all, he said rather pointedly, “Although I have the full right in Christ toorder you to do what is proper, I rather urge you out of love” (Phlm 8-9). Only people in authority can issue orders.
Answered by: Catholic Answers Staff
In Acts 15: 12-21 It was James who made the judgment concerning the problems between the Jews and Gentiles. Paul reports to James (Acts 21:17-19) concerning his work among the Gentiles.
Act 6. Here Peter got up and Speak. “THE WHOLE ASSEMBLY IS SILENT” you know why? because Peter has spoken and it is final. James is just repeating what Peter has already decided. If he contradicts Peter’s position then we have an issue. But no, he merely approves of it. James was the bishop of see of Jerusalem by the way. Some councils even have the Pope not in attendance, but have to be approved by the see of Rome.
6 The apostles and elders met to consider this question. 7 After much discussion, Peter got up and addressed them: “Brothers, you know that some time ago God made a choice among you that the Gentiles might hear from my lips the message of the gospel and believe. 8 God, who knows the heart, showed that he accepted them by giving the Holy Spirit to them, just as he did to us. 9 He did not discriminate between us and them, for he purified their hearts by faith. 10 Now then, why do you try to test God by putting on the necks of Gentiles a yoke that neither we nor our ancestors have been able to bear? 11 No! We believe it is through the grace of our Lord Jesus that we are saved, just as they are.”
12 The whole assembly became silent as they listened to Barnabas and Paul telling about the signs and wonders God had done among the Gentiles through them. 13 When they finished, James spoke up. “Brothers,” he said, “listen to me. 14 Simon[a] has described to us how God first intervened to choose a people for his name from the Gentiles. 15 The words of the prophets are in agreement with this, as it is written:
16 “‘After this I will return
and rebuild David’s fallen tent.
Its ruins I will rebuild,
and I will restore it,
17 that the rest of mankind may seek the Lord,
even all the Gentiles who bear my name,
says the Lord, who does these things’[b]—
18 things known from long ago.[c]
19 “It is my judgment, therefore, that we should not make it difficult for the Gentiles who are turning to God. 20 Instead we should write to them, telling them to abstain from food polluted by idols, from sexual immorality, from the meat of strangled animals and from blood. 21 For the law of Moses has been preached in every city from the earliest times and is read in the synagogues on every Sabbath.”