The NT church never taught that
Peter was the "rock" of Mt. 16:18 upon which the church is built, interpreting Mt. 16:18, rather than upon the rock of the faith confessed by Peter, thus Christ Himself.
For in contrast to Peter, 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) Rome's current catechism attempts to have Peter himself as the rock as well, but also affirms: “On the rock of this faith confessed by St Peter, Christ build his Church,” (pt. 1, sec. 2, cp. 2, para. 424) which understanding some of the so-called “church fathers” concur with.)
But which is just one of the many distinctive Catholic teachings are not manifest in the only wholly inspired substantive authoritative record of what the NT church believed (which is Scripture, in particular Acts through Revelation, which best shows how the NT church understood the gospels).
In that time giving the keys implied giving authority. Read Isaiah 22 about Eliakem. You assume Jesus meant Peter’s faith instead of actually loo EWTN Bible 2 Thessalonians 2:15 15 So then, brethren, stand firm and hold to the traditions which you were taught by us, either by word of mouth or by letter. king at what he said.
Also in the NT there is only one church they and it continues as an unbroken chain from the 12 Disciples through the Bishops of the church. It is only the Catholic Church that continues from Jesus Christ to today and as you see from the NT the church Jesus established is the pillar and bulwark of the truth.
1 Timothy 3:15 if I am delayed, you may know how one ought to behave in the household of God, which is the church of the living God, the pillar and bulwark of the truth. The church is the pillar and bulwark of the truth not the NT.
Read the early church fathers and you will see the church in the NT is the Catholic Church.