This short passage generates a considerable degree of contention, particularly regarding the difference between “petros” and “petra”. The problem is that they are different words. The first is a masculine noun most commonly used for small, separate pieces of stone. The second is a feminine noun most commonly used for large areas of stone.
Concerning this difference, the argument made by some Protestant apologists is that it clearly shows that Peter was not the one upon whom Jesus was planning to build his Church, which undercuts the Catholic claim about the primacy of the leader of the Roman Church as the descendant of Peter. The response made by some Catholic apologists is that the difference is nothing more than a linguistic necessity: Peter was male, and so Matthew could not use a feminine name for him (Jesus was speaking, but in Aramaic; the Greek is Matthew's). Other Catholic apologists say that the two different words were used merely to avoid repetition. They also say that “petros” and “petra” are really the same noun, just masculine and feminine forms of one thing.
I unashamedly admit to finding this all rather interesting, and so I shall now proceed to bore you with a couple of thoughts on the matter. Firstly, the comment that the two nouns are the same is dubious at best. Any who uses a language with genderised nouns can tell you that the distinction between a masculine noun and a feminine one is a significant, even vital conceptual difference, but it is not a biological one: feminine nouns do not necessarily indicate female things. When was the last time that you saw a female rock? Further, the claim that Matthew was shy about using a feminine noun for Peter makes one wonder why this alleged shyness did not spread to Paul, who had no qualms about using a feminine noun for Jesus (in 1 Co 10:4, later), or why no one had any problem using the neuter noun “probaton” (sheep) for Jesus or his believers. Very shortly after commending Peter in Mt 16:18, Jesus calls him “Satanas” (Satan; v.23), which is far worse than using a noun of the feminine class.
This distinction between “petros” and “petra” is then carried over into the fact that they are used differently within the New Testament texts. “petra” is used 16 times: the rock upon which the wise man builds his house; the rock which is rent when Jesus dies; the rock from which the tomb was hewn; the rock upon which the sower threw the seed which then withered; the rock of offense (from Isaiah 8:14); the rocks among which the kings of the earth hide when the Lamb opens the sixth seal; the spiritual drink-giving rock which was Christ. “petros”, on the other hand, is only ever used for Peter. If the two words were interchangeable, it would be reasonable to assume that they would be used interchangeably; this would, after all, concur with the view that the difference in Mt 16:18 is merely for the sake of variety. Far from being interchanged, “petra” is privileged, so much so that, in four locations, we find it used twice in quick succession: in Matthew 7:24-5 and Luke 6:48, in Revelation 6:15-6, and in 1 Corinthians 10:4. The usage in Matthew and Luke tells of where the sower scattered the seed. That in Revelation is where the kings hide. The double occurrence in 1 Corinthians is the spiritual drink-giving rock, Christ, now represented by a feminine noun. The writers of the New Testament did not use the words “petros” and “petra” interchangeably.
In fact, there is another word that is interchanged with “petra”: “lithos”. This one shows up some 60 times in the NT, in a variety of situations, but most noticeably as the 'other' stone in references to Christ as “lithos proskommatos kai petra skandalou” (a stone of stumbling and a rock of offence), in Romans 9:33 and 1 Peter 2:8. Not only is a feminine noun used to describe Christ (again), but both a masculine one and a feminine one are used, as if there is no significance to the gender-class of the noun. Again using “lithos”, both Christ and believers are described as 'living stones' in 1 Pe 2:4-5. This is a masculine noun for stone, which is used for people, and has a meaning which is interchangeable with “petra”: it has all of the qualifications which would meet the Catholic apologists' justifications for using “petros” rather than “petra”. Why not use “lithos” instead of “petros”? For that matter, why not use the masculine noun “pagos” (as in Areopagos) instead of “petra”, since it would then more closely echo the idea of the Temple Mount, upon which the original church was built?
We can reasonably discount the claims that “petros” was used simply because it is masculine, or because it is interchangeable with “petra”. Where that leaves us is with the usage of two different nouns. Unfortunately for the Protestant apologists, this does not, in any way, disprove the Catholic claim about the primacy of the leader of the Roman Church as the descendant of Peter. All it serves to do in that respect is render highly suspect any such claim which is based upon this verse alone.
All of this has been a discussion of the text. Jesus, as mentioned earlier, did not speak Greek and said neither “petros” nor “petra”; he spoke Aramaic and said, “cephas”. The writer of Matthew used two words which are similar, yet different, creating a verbal relationship which would have been immediately and vividly apparent to a contemporary reader in a way that the use of either “lithos” or “pagos” would not have been. As for the motivation behind it, I will leave that up to you.