The Pope is considered the head of the Church (Catechism 883) altho the Bible teaches something quite different. Eph. 5:23 “Christ is the head of the church”; Col.1:17-18 “And He is before all things, and in Him all things consist. And He (Christ) is the head of the body, the church.” The Pope is called the only authority over the church (Catechism 816). We find Peter considered himself a fellow elder (one among many) and is treated this way throughout Scripture(1 Pt.5:1-2). He is not the apostle over all the other apostles. In Peter's 2nd epistle he states he is an apostle, not THE apostle. In Gal.2:9 he is named as one of the pillars, not THE pillar, and James is mentioned first and John last. Leadership in the New Testament is always plural, never singular. Peter makes no unique claims for himself but calls himself an eyewitness with the other apostles 2 Pt.1:16. One cannot find this claim of being in charge coming from his own mouth.
Catholicism has it's members call their priest "father", for example when confessing to a priest they start out by saying "father forgive me for I have sinned" That use of "father" directly contradicts the Bible: Matthew 23:9 And call no man your father upon the earth: for one is your Father, which is in heaven.
The word Petra for rock is used 16 times in the New Testament. 11 times of a massive cliff rock, a bedrock, 5 times symbolically of Christ himself. (Eg. 1 Cor.10:4 The rock in the wilderness is Christ)
The name Peter (Petros) a masculine noun means small rock or stone. Mt. 16:18 is the first time it is used saying “I will build my church”, a future event when the Spirit is sent and the body of Christ is formed. Jesus said “ I say unto you ,you are Peter (Petros) and upon this Rock (Petra feminine noun meaning a massive rock) I will build my church.” First we see who the rock is, second we see it is Jesus building the church not Peter. It is Jesus who states I will build my church, he protects it and gives increase to it. If Jesus were actually referring to Peter as the rock, Jesus would have used the masculine word petros for the rock. Jesus instead used a different Greek word for “this rock” a feminine word petra indicating something other than Peter. Since the Holy Spirit guided the apostles writings into all truth we should expect the precise words used to convey the meaning (John 14:26; 16:13). Arguments such as they spoke in Aramaic don't hold up either. Maybe they did speak this language but it was written in the Greek and therefore the distinction. The ones that were there and heard what Jesus said wrote it in Greek.
The Scripture also states the Church is also built upon the foundation of the apostles who were connected directly to Christ (Eph 2:20). The first stones of that building (the church) were laid next to the chief cornerstone (the rock) by their ministry. We find their names written in the foundations of the new Jerusalem, (Rev. 21:14). Notice they are collectively together, nowhere do we find Peter separately. Petros means a (piece of) rock; but the Scripture is saying very clearly Peter is related to the Rock because of his confession, not the rock himself. And he is not the only one to have this confession. The true rock (Petra) is massive.
It was not Peter who was the rock, for the Old Testament of which both he and Paul both agree on explains who the rock is. Ps.18:31: “For who is God save the LORD? or who is a rock save our God?" Throughout the Old Testament the rock was synonymous with God 2 Sam 22:32: “For who is God, except the LORD? And who is a rock, except our God? Deut 32:15: “Israel forsook God who made him, and scornfully esteemed the Rock of his salvation.” Deut 32:18: “Of the Rock who begot you, you are unmindful, and have forgotten the God who fathered you.” Ps. 62:2: “He only is my rock and my salvation” Ps. 95:1: calls God, “the Rock of our salvation.” No human being was ever referred to as a rock in the Old Testament Hebrew Scriptures, neither are they found in the New Testament. The “Rock” (stone, cornerstone) is reserved only for Jesus Christ (Matt 21:42; Isa. 28:16; Cor. 3:11; 10:4; Eph 2:20; 1 Peter 2:6-8).
Isa. 44:8: “Is there a God besides Me? Indeed there is no other Rock; I know not one.” This should settle any idea of anyone else being called the foundation stone for the Church. The Popes say that Peter was the rock, but Peter himself said Jesus is the rock (1 Peter 2:4-8). He even preaches this to all of Israel in Acts 4:11 speaking of Christ, “This is the stone the builders rejected (Christ) which has become the chief cornerstone”, he then proclaims there is salvation in no other “for there is no other name under heaven given among men by which we must be saved.” That rock is our salvation, this is what the Church is built upon. Salvation is found in the person of Christ not in the church or in sacraments. It is found in the rock just as Jesus said, he would build his church on this confession. The rock was the confession of Peter’s revelation, this is the very reason why he is commended. This is something the Father testified all through Christ’s ministry. Sometimes it was audible like at the baptism and the transfiguration when the Father spoke “this is my beloved son” and accompanied it by supernatural signs. It is this confession of Jesus being the Son of God that the universal church is built on.
Another question about Peter would be: was only Peter given the keys of the kingdom (Mt.16:19). “I will give you the keys of heaven,” if this means it is to Peter only, then there can be no Roman Catholic justification for it being given to anyone afterwards. Yet there is no Scripture that entertains this idea of apostolic succession.
“I will give you the keys” at the time was future tense, meaning after Jesus' resurrection; when He ascended on high, He gave those gifts (Eph. 4:8) empowered the apostles with the Holy Spirit so they may employ their authority under Christ. Peter had the pronouncement of the keys given to him first but not him alone. This power of authority was actually given, not to Peter only, but to all the apostles. This is a delegated spiritual power; it is a power pertaining to all the things of the kingdom of heaven. The figure of the keys is of a building with keys that are used to open from the outside. Jesus gives to Peter the keys of the kingdom of heaven, meaning that he will make him the instrument of opening the door of faith to the world, first to preach the gospel to the Jews and then the Gentiles. In this way what is bound on earth is bound in heaven.
To “bind and loose” in the vernacular of the Jews at that time, signified to prohibit and permit; to teach or declare a thing to be unlawful was to bind; to be lawful, was to loose. As the leadership was ripped from non believing Israel and given to the apostles; some things forbidden by the law of Moses were now to be allowed, as the eating of such and such meats; some things allowed there were now to be forbidden. Acts 10:13-16 And a voice came to him, “Rise, Peter; kill and eat.” But Peter said, “Not so, Lord! For I have never eaten anything common or unclean.” And a voice spoke to him again the second time, “What God has cleansed you must not call common.” This was done three times. And the object was taken up into heaven again.” By God loosening the restrictions permitting non kosher foods to be eaten Peter understands the vision through the gentiles. Peter used these keys in a legislative sense of ‘loosing' as Peter saw God’s spirit moving to declare the gentiles clean. Just as it was revealed to him previously by a vision in Acts 10:9-48. The Lord was telling him to eat what was on the sheet. Peter refused because it was forbidden to eat unclean animals under the Mosaic Law. After three times of the Lord saying to eat because they are now clean, Peter then begins to contemplate what the vision meant. This had a two-fold meaning showing that the foods once forbidden were now permitted and from this Peter realizes that the Lord had cleansed all by his blood so the gentiles can also be saved.
The Bible makes it clear the foundation of the church is not on one apostle but all of them. Eph 2:20 “having been built on the foundation of the apostles and prophets, Jesus Christ Himself being the chief corner stone.” It is not built on Peter as Roman Catholicism claims. In heaven as on earth God recognizes them equally. “Now the wall of the city had twelve foundations, and on them were the names of the twelve apostles of the Lamb.” There is not Peter with the eleven, he is included with the twelve.( Rev 21:14)