Definitions (from Vine’s expository dictionary): Petra denotes "a mass of rock," as distinct from Petros, "a detached stone or boulder," or a stone that might be thrown or easily moved.
Matthew 16:18: “And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.” The Catholic Church uses this verse as justification for its teaching that the pope holds the office Peter once held, with Peter being the rock upon which Jesus would build His church. The Greek word translated “rock” in Matthew 16:18 is Petra, which refers to a massive boulder and a firm foundation.
John 1:42: “And he brought him to Jesus. And when Jesus beheld him, he said, Thou art Simon the son of Jona: thou shalt be called Cephas, which is by interpretation, A stone.” The word translated Cephas is Kephas, or “stone”.
The Catholic Church makes a connection between Jesus’ giving Peter the name “Cephas” and the rock He mentions in Matthew 16:18. In his website Mario Derksen explains the Catholic Church’s belief regarding the meaning of Petra and Petros: “With that in mind, namely, that Simon is the Greek Petros and the Aramaic Cephas, we can now proceed to further clarify who is the rock of Matthew 16:18 upon whom or which the Church is built. Now, the Aramaic cephas means "rock," and "rock" ONLY; it does NOT mean "stone." Therefore, we conclude that when Jesus said that Simon was now Peter, He meant to apply the title "rock," Petra in Greek, to him, since the other translation of "Peter" is Cephas, which means "rock." So Christ built His Church "upon this rock"--Peter. The reason Jesus did not call Simon Petra is very simple: the word Petra has a feminine ending because it is a feminine noun. It is not appropriate to give a male person a female name. So Jesus makes this female noun "male" by switching the female -a ending into the male -os ending, so that the Greek word "rock" can be applied to Simon. Again, we know that Jesus means to call Peter ROCK and not STONE because in Aramaic He calls him Cephas, which can only mean "rock" and not Evna, which is the Aramaic name for "stone," and because he could have called him Lithos instead, the Greek word for "stone," which even possesses a male ending already.” (http://www.cathinsight.com/apologetics/adventism/peter.htm) So according to the Catholic Church, the reason Jesus called Peter the Aramaic Cephas (Greek Petros, a stone that is easily moved) and not Petra (a massive boulder) is because it would have been inappropriate for Him to assign a name with a feminine ending to Peter, who was a man. There are a few problems with this reasoning:
Natural gender (Grammar points taken from William Mounce’s Basics of Biblical Greek, page 24): The Catholic Church has misinterpreted these verses because of their insistence that the gender of the noun used to describe Peter match his gender. This is called natural gender. Natural gender means that a word takes on the gender of the object it represents. In Greek, pronouns follow natural gender but nouns for the most part do not. Both Petros and Petra are nouns! In Greek, these words generally do not follow natural gender. For example, the Greek noun for sin is hamartia. This is a feminine noun. However, we all understand that this word may be used to describe the state of either a man or a woman. Hamartia does not follow natural gender when it describes the sinful state of a man (rather than a woman). In a similar fashion, the nouns Petros and Petra are used to describe characteristics of a person regardless of their gender. Petros was used to describe Peter because he manifested the characteristics of a small pebble.
Other uses of Petra:
1 Corinthians 10:4: “And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ.” “Rock” is the Greek Petra, and Paul states plainly that this Rock was Jesus Christ. However, Jesus was a man (i.e. of the masculine gender)! The fact that Paul uses Petra (a feminine noun) to describe Jesus (a man) shows that it is unnecessary for nouns to follow natural gender in the Greek language. The noun describes a characteristic of the person.
1 Peter 2:7-8: “Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner, And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed.” Petra is translated “rock” in these verses. Acts 4:10-11 tells us specifically who is this “head of the corner”: “Be it known unto 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 whole. This is the stone which was set at nought of you builders, which is become the head of the corner.” So again, we have the feminine Petra being used to describe Jesus Christ, emphasizing the fact that the gender of a Greek noun does not need to match the gender of the one it describes.
So in these verses and the way the Catholic Church interprets them we see that the entire superstructure of the Catholic Church is based on error. Jesus did not build His church upon Peter, He built it upon the confession Peter made in Matthew 16:16. I’ve gone over this passage in Matthew in detail in my article published elsewhere on my website. Follow this link and you'll be taken to it.