Καγω δε σοι λεγω, οτι συ ει Πετρος, και επι ταυτη τη πετρα οικοδομησω μου την εκκλησιαν, και πυλαι αδου ου κατισχυσουσιν αυτης. Matthew 16.18, Greek

It is highly likely that Matthew originally wrote his Gospel, or at least some portion thereof, in Hebrew or Aramaic. See Hebrew of Matthew.

It is unknown when Matthew was first translated into Greek, or by whom, or if, perhaps, Matthew himself wrote it also in Greek. Jerome says, "but this was afterwards translated into Greek though by what author is uncertain." See Jerome, Lives of Illustrious Men, Chapter III.

This single verse of Scripture is the foundation upon which is laid all of Rome's claims to papal primacy, pre-eminence, infallibility, jurisdiction, etc. In fact, the very existence of the papacy, as distinct from every other bishopric in the Church, stands or falls upon the validity, or the invalidity, of Rome's interpretation of this verse of Scripture.

According to Rome's interpretation, Peter (gr. petros) and the 'rock' (gr. petra) are one and the same. This, in spite of the fact that the two words carry different meanings.

"In secular Greek pétra denotes a large 'rock,' but also a 'cliff'; or 'rocky mountain chain.' Figuratively it suggests firmness, immovability, and hardness. pétros is more often used for smaller rocks, stones, or pebbles."
Theological Dictionary of the New Testament, by Geoffrey W. Bromily. © 1985 by William B. Eerdmans Publishing Company

Rome says that the reason Peter is called petros is because petros is the masculine form of the feminine noun petra (meaning 'rock'), and it was fitting that Peter's name should be masculine. However, I have never seen them offer an explanation for why the feminine petra is always used in the Scriptures to refer to Christ, but never the masculine petros, which is only used to refer to Peter. I believe it is because, by definition, petra more accurately typifies Christ, while petros more accurately typifies Peter. It is upon the petra that Christ is building his Church.

But Rome claims that, on the basis of this verse of Scripture, Peter is the 'rock' on which Christ is building his Church, and that the honor accorded to Peter alone is the rightful heritage of the bishops of Rome whom, they claim, are the successors of Peter and the 'vicars' of Christ. Further, they claim that, therefore, the bishops of Rome are endowed with primacy over all other bishops, infallibility in doctrines of faith and morals, and supremacy and jurisdiction over all the members of Christ's Body, the Church. See Matthew 16.18 for some examples from Vatican I & II of these claims.

In taking this position, Rome ignores the fact that Peter tells us that Christ is the Rock on which we are being builded:

3 If indeed ye have tasted that the Lord is gracious.
4 ¶ To whom coming, as to a living stone, rejected indeed by men, but chosen by God, and precious,
5 Ye also, as living stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ.
6 Therefore also it is contained in the scripture, Behold, I lay in Zion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded.
7 To you therefore who believe he is precious: but to them who are disobedient, the stone which the builders rejected, the same is made the head of the corner,
8 And a stone of stumbling, and a rock [petra] of offence, even to them who stumble at the word, being disobedient: to this also they were appointed.
(I Peter 2.3-8).

Peter tells us from the very earliest days of the infant Church that Jesus is the Rock on which the Church is being built (Acts 4. 10-12):

10 Be it known to you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you sound.
11 This is the stone which was set at naught by you builders, which is become the head of the corner. (Psalm 118.22)
12 Neither is there salvation in any other: for there is no other name under heaven given among men, by which we must be saved.

In I Peter 2.6 and Ephesians 2.20, Christ is called the Chief Cornerstone of the foundation. The Greek word here is akrogoniaios, or the 'extreme corner'. Rome claims that this means the 'capstone', which could be a possible translation of the word in another context—but not in this context. Holding this view enables them to continue to maintain the view that Peter is the foundation 'rock' upon which the Church is builded. But that is not an honest interpretation of this passage of Scripture. For the quote referenced here is Isaiah 28.16, where it speaks of a foundation stone:

Therefore thus saith the Lord GOD, Behold I lay in Zion for a foundation a stone, a tried stone, a precious corner stone, a sure foundation: he that believeth shall not make haste.

Thus it is clear that Christ, and not Peter, is the Chief Cornerstone of the foundation, and the Rock, on which the Church is being built.

What could be more clear? Rome has no excuse for not seeing and teaching these things. But it simply does not fit their plan.

The Greek petros is used in the New Testament only for Peter's name. The only possible exception to this is John 1.42, where petros is sometimes translated Peter, and sometimes a stone.

Petra, translated 'rock', is found sixteen times in the New Testament. Besides Matthew 16.18, four other of those times it speaks of Christ (Romans 9.33; 1 Corinthians 10.4 - twice; 1 Peter 2.8). Four times it speaks of Christ's word (Matthew 7.24, 25; Luke 6.48 - twice). Two times it speaks of the sepulchre where they laid Jesus (Matthew 27.60; Mark 15.46). Two times it is the rock upon which the seed fell in the parable of the sower (Luke 8.6, 13). Three times it speaks of the rocks of the mountains, or of the earth (Matthew 27.51; Revelation 6.15, 16).

Paul quotes the passage out of Isaiah 28.16 in his letter to the Romans 9.32-33, saying that it speaks of Christ:

32 Why? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
33 As it is written, Behold, I lay in Zion a stumblingstone and rock (petra) of offence: and whoever believeth on him shall not be ashamed.

It is made clear in 3 of the Gospels, and in the Book of Acts, that Psalm 118.22 speaks prophetically of Christ as the Stone, rejected by the builders, that was made the Head of the corner (Matthew 21.33-44; Mark 12.1-12; Luke 20.9-18; Acts 4.10-11).

And Paul writes in 1 Corinthians 10.4 that Christ is the Rock:

4 And all drank the same spiritual drink: for they drank of that spiritual Rock (petra) that followed them: and that Rock (petra) was Christ.

Paul writes in Ephesians 2.20 that Christ is the Chief Corner of the foundation:

20 And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;

And Paul writes in 1 Corinthians 3.10-11 that Christ is the foundation upon which we must build:

10 According to the grace of God which is given to me, as a wise masterbuilder, I have laid the foundation, and another buildeth upon it. But let every man take heed how he buildeth upon it.
11 ¶ For other foundation can no man lay than that which is laid, which is Jesus Christ.

And then there are the popish apologists and Greek exegetes, like this one, who says:

Apart from translations others try to say that when Jesus said "and on THIS rock I will build My Church" he was actually referring to himself. This is another big mistake, when a demonstrative pronoun is used with the Greek word for "and", which is "kai", the pronoun refers back to the preceding noun. In other words, when Jesus Says, "You are rock, and on THIS rock I will build My Church", the second rock He refers to HAS to be the SAME rock and the first one. Peter is the Rock in BOTH cases.

This is what could be called bad Greek. In fact, it could be called complete nonsense. It is not any rule of Greek grammer; and it does not offer any explanation why the sentence goes from second person masculine to third person feminine, if both nouns refer to Peter. The switch to the third person, while still speaking to Peter, seems to indicate that the rock is something other than Peter.

How strong are the delusions of papal idolatry that cause people to willingly invent such reasonings, and others to blindly place their faith and trust and confidence in them. But, Christ said that the blind follow their blind leaders into the ditch.

The feminine demonstrative pronoun taute is used 31 times in the New Testament (including Matthew 16.18). Five of these times it is in close proximity following kai. In none of these five instances (including Matthew 16.18) does it refer back to a precedent noun. Taute, in these instances, always and only refers to the noun which it modifies, which in the case of Matthew 16.18 is "rock". The five instances are:

1. Matthew 12.45: Even so shall it be also (kai) to this (taute) wicked generation.

2. Matthew 16.18: That thou art Peter, and (kai) upon this (taute) rock I will build my church

3. Luke 19.42: If thou hadst known, even (kai) thou, even (kai) at least in this (taute) thy day

4. II Corinthians 1.15: And (kai) in this (taute) confidence I intended

5. II Corinthians 8.7: that ye abound also (kai) in this (taute) grace.

While there may be instances where a demonstrative pronoun can refer back to a precedent noun (e.g. Matthew 21.23), it surely is not a grammatical rule in Greek that it must—nor even that it most often does.

A more capable examination of this passage can be found in the treatise The Rock of the Apostle Peter, by Panagiotis Boumis (Translated by David Turner), wherein it is shown that the passage can properly be interpreted as Christ being the Rock on which the Church is built—and that there is reason for so interpreting it.

At first, we cannot exclude the interpretation that the "Πετρα" named by the Lord is the confession about Christ ως Υιον του Θεου του ζωντως, or rather Jesus Christ Himself. This very formulation of the passage allows for just such an interpretation. The passage, as is known, runs, Καγω δε σοι λεγω οτι συ ει Πετρος, και επι ταυτη τη πετρα οικοδομησο μου την εκκλησιαν, and not συ ει Πετρος και επι σε οικοδομησο μου την εκκλησιαν. Thus we can say that this change in the term (Πετρος - Πετρα) in the two sentences, in conjunction with the existence of the preceeding confession Συ ει ο Χριστος, ο υιος του Θεου του ζωντως not only provides us with a possibility but also a reason to render this passage in the above mentioned interpretation.

The writer goes on to explain that it is also not impossible to understand Peter as being the rock—but not to the exclusion of the other apostles, who all are rocks in the foundation of the Church (e.g. Ephesians 2.20; Revelation 21.14). He concludes his discussion like this:

In retrospect, one may say that the clearest interpretation of και επι ταυτη τη πετρα οικοδομησο μου την εκκλησιαν is the following: I will build my Church also on this rock, in which you confessed, that Jesus Christ, as upon solid ground and on you, Peter, as confessing in Him and constituting thus a foundation stone on this ground, without excluding but rather understanding that I will also build on other foundation stones, namely the rest of the Apostles, who will proclaim the same truth in Christ upon whom will rest the teachings of the Church concerning me.

There is nothing in the New Testament that gives any support to the thought that Peter was given any place of pre-eminence above the other apostles in the Church, or that he is the 'rock' upon which the Church is being built. Peter, James, and John were at times present with Christ apart from the others: the Transfiguration, the healing of Jairus's daughter, Gethsemane; and, at times, Peter acted as a leader among the disciples. But it is a far stretch from that to claim that Peter is the rock on which Christ builds his Church—especially when the weightier evidence indicates that Christ Himself is that Rock. Peter, in humility, would rather have had the attitude of John the Baptist who said of Christ, "He must increase, but I must decrease." (John 3.30) Rome has rather ever and always sought to increase itself to the disparagement of Christ and the rest of the Church.

See also Peter's Equality. All of the aforementioned Scriptures lend support to the understanding that Christ, not Peter, is the 'Rock' upon which the Church is being built.