But the Peter of Scripture was a believer in the Lord who established His claims upon Scriptural substantiation in word and in power, as did His apostles, and thus we need to examine what being given the keys to the kingdom meant, and who "upon this Rock" applies to, the in the light of the rest of the NT.
the keys of the kingdom of heaven
In which we see that it is by believing the gospel that one enters the kingdom of God, "Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son," (Colossians 1:13) and which keys Peter, as the street-level leader among the brethren (over whom he never manifestly exercised authority) first used on behalf of both Jews and Gentiles. (Acts 2;10) But which was not exclusive to Peter, as the whole scattered church "went preaching the word," while the apostles remained in Jerusalem. (Acts 8:4,14) And the Lord also sanctioned (after reproving the apostles for reasoning who would be greatest among themselves) such as manifestly did ministry in His name but who operated independent of the apostles. (Lk. 9:49)
authority to bind and loose on earth.
But which also was not exclusive to Peter, but is applied to the whole church, (Mt. 18:15-20) and understood such as exercised in 1Co. 5 in which Paul (who received his gospel and commission directly from the Lord, later affirmed by men, and power thru the certain devout disciple Ananias), "In the name of our Lord Jesus Christ, when ye are gathered together, and my spirit, with the power of our Lord Jesus Christ," (1 Corinthians 5:4) delivers an incestuous man (whom the church failed to discipline) over to the devil for chastisement. (cf. 1Tim. 1:10) And says that if they forgive any thing, he forgives them also in the person of Christ. (2Co. 5:10)
Nor is thsi power of binding and loosing new, but flows from the OT magisterium, dissent from whose binding or loosing judicial judgments was a capital offense. (Dt. 17:8-13) But
And besides formal judicial magisterial judgments together with the church, spiritual power of binding and loosing is provided for all believers of holy fervent faith like that of Elijah, who bound the heavens from raining for 3.5 years and then loosed them to do so later. "Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much." (James 5:16). Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven. For where two or three are gathered together in my name, there am I in the midst of them. (Matthew 18:19-20) )
the one holy catholic apostolic church is built on the foundation of Kephas,
Which is first a linquistical argument, which (since the Lord did not say "upon this Kephas I will build my church") presumes the Lord was speaking Aramaic, but which, unlike certain other cases, the Spirit chose not to record it as but choose Greek, and which makes a distinction btwn petros and petra, resulting in an endless and ongoing linquistical debate.
However, the answer is to be found in what the rest of the NT reveals as concerns Peter being the stone/rock upon with the church is built or Christ, and after that of Peter particularly being the foundation of the church.
In which nowhere interpretive of Mt. 16:18 is Peter called or described as the Rock upon which the church was built. Instead, that the LORD Jesus is the Rock (“petra”) or "stone" (“lithos,” and which denotes a large rock in Mk. 16:4) upon which the church is built is one of the most abundantly confirmed doctrines in the Bible (petra: Rm. 9:33; 1Cor. 10:4; 1Pet. 2:8; cf. Lk. 6:48; 1Cor. 3:11; lithos: Mat. 21:42; Mk.12:10-11; Lk. 20:17-18; Act. 4:11; Rm. 9:33; Eph. 2:20; cf. Dt. 32:4, Is. 28:16) including by Peter himself. (1Pt. 2:4-8)
Which leaves RCs relying on Ephesians 2:20: "And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone." But Peter is not mentioned here, nor is submission to, or remembrance of Peter as the supreme head of the church enjoined or commended.in any of the instruction to the churches (Romans to Revelation), and is rarely even mentioned (contrary to Rome), not even in Romans among the over 30 persons mentioned. Nor it is exampled in the life of the NT church, as it is James who delivers the Scripturally substantiated doctrinal and disciplinary final judgment in Acts 15, confirmatory of what Peter exhorted and testified to, which Paul and Barnabas taught and also testified to.
Thus the issue is not that Peter was the leader among the 11, but that the manner of leadership is not that of Rome, which even Catholic (among others) scholars testify against, even before Constantine.
And critically, the NT church never manifestly saw apostolic successors being voted for after Matthias was chosen for Judas (even though James was martyred: Acts 12:1,2), which was in order to maintain the foundational number of apostles (cf. Rv. 21:14) and which was by the non-political Scriptural means of casting lots. (cf. Prov. 16:33)
At least you admitted that the Messiah gave someone, the Apostle Peter directly, the power to bind and loose on earth. Not only that, you admitted the whole (one holy catholic apostolic church) assembly of Apostles, including those eligible to be Apostles and those in communion with them. was given this authority. You also linked it to the Jewish origins of binding and loosing. You have admitted much here. Now, any gainsaying aside, it is simply a matter of succession and provenance.