The original words (spoken by Jesus) were Aramaic: as is made plain in John 1:42 St Peter was called ‘Cephas’
John 1:42 would indicate that it was originally in Aramaic.
The words really don’t matter; the MEANING of the entire passage DOES!
Both David Garland (“Reading Matthew: A Literary and Theological Commentary on the First Gospel”, New York: Crossroad Publishing, 1995) and Everett Ferguson (“The Church of Christ: A Biblical Ecclesiology for Today”, Grand Rapids/Cambridge: Eerdmans Publishing Co, 1996) point to the 1990 study by C.C. Caragounis, “Peter and the Rock” (Berlin: Walter de Gruyter)
Here are Garland’s finding:
C.C. Caragounis’s study of this passage carefully argues, however, that the rock refers to something other than Peter. The demonstrative pronoun “this” [in the phrase “on this rock”] logically should refer to something other than the speaker or the one spoken to and would be appropriate only if Jesus were speaking about Peter in the third person and not speaking to him. If Jesus were referring to Peter, it would have been clearer to have, “You are Rock, and upon you I will build my church” (Caragounis 89). Petros usually meant a free-standing “stone” that could be picked up; and petrausually was used to mean “rock,” “cliff,” or “bedrock.” But the two terms could reverse their meaning and no clear-cut distinction can be made between the two (Caragounis, 12, 15). If the two words were intended to refer to the same thing, petros could have been used in both places since it could be used to mean both stone and rock. The use of two different terms in the saying, petros and petra, implies that the two were to be distinguished from each other. More>
Though it certainly it is well supported that the Lord spoke Aramaic as well as Greek (a the common language of Palestine at that time), Hebrew and perhaps Latin, that He mainly spoke one of the forms of Aramaic to His disciples, and especially in Mt. 18, is not certain. Richard A. Horsley in “Galilee: History, Politics, People,” states, “It is difficult in the extreme to interpret the fragmentary evidence available and draw conclusions for the use of languages in late second-temple Galilee” (p. 247).
Although Aramaic may have been the most common tongue, yet a survey covering 700 BC to 300 AD did find, "Of all Hebrew inscriptions from the Mediterranean world, 68 percent are in Greek, 18 percent in Hebrew or Aramaic, 12 percent in Latin, and 2 percent are bilingual." If we omit those from the Holy Land: 85 % Greek, 10% Latin, 5% in another language.. — Pieter van der Horst, Ancient Jewish Epitaphs, in Contributions to Biblical Exegesis and Theology 2 Kampen Kok Pharos, 1991. Reviewed in CBQ, July 1993. https://www.ewtn.com/library/SCRIPTUR/LANGPAL.TXT
Simon needed a new name, as Simon was a common name by the Second Temple Period, and unlike the rest, it is omitted from Moses’ blessing in Deut. 33, and it produced no judges or kings
“the currency of Peter's name is confirmed in Tal Ilan's identification of three additional first and second-century Palestinian Jewish individuals who bear the name Petros.* — http://www.jjs-online.net/doc.php?id=055_01_058_1
It is worth noting that the Palestinian Talmud and midrashim repeatedly feature an early Amoraic Rabbi Yose ben Petros, whose father constitutes proof that even this Greek name was by no means unknown in the early rabbinic period.
Some scholars have suggested an Aramaic background to Jesus’ saying. Joseph A. Fitzmyer, Professor Emeritus of The Catholic University of America in Washington, D.C., and one of the world’s most distinguished New Testament scholars, suggests that Jesus employed an Aramaic wordplay (Kepha-kepha) in his response to Peter’s declaration.[3] However, Fitzmyer acknowledges a difficulty: he wonders why the Matthean Jesus did not say, “On this petros I will build….”[4]
[4] Substituting the Greek masculine petros for the Greek feminine petra, the reading of all Greek manuscripts. See Fitzmyer, ibid., pp. 130-131: “The problem that confronts one is to explain why there is in the Matthean passage a translation of the Aramaic substratum, which is claimed to have the same word kepha twice, by two Greek words, πέτρος and πέτρα… If the underlying Aramaic of Matt. xvi.18 had kepha twice, then we should expect σὺ εἶ Πέτρος, καὶ ἐπὶ τούτῳ τῷ πέτρῳ οἰκοδομήσω….” Cf. Fitzmyer’s recent comments in response to a magazine reader’s letter (“Queries & Comments,”Biblical Archaeology Review 19.3 [1993], 70). For Fitzmyer’s Aramaic reconstruction to be correct, the Greek text should read, “on this petros I will build….”
[5] The word כֵּפָא (kepha). The only difference between Kepha and kepha in Fitzmyer’s reconstruction is the capitalization of the former. This distinction, however, does not exist in Aramaic, since in Aramaic there are no capital letters. - http://www.jerusalemperspective.com/2718/
In any case, the linguistical debate is endless and on going, while the answer is to examine what was said in context and how this is understood in the rest of Scripture.
If Peter was called the Rock upon whom the church was continually built and was thus looked as that, rather than “this rock” in Mt. 16:18 referring to the truth of Peters confession and by extension Christ, then we most certainly would see this affirmed in the rest of the NT. However, 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 ancients concur with.
The Catholic imagination knows no bounds when they need to argue for something that is not in Scripture, but , Peter as being the infallible Roman rock upon which the church is continually built is simply not what the Holy Spirit reveals in the rest of Scripture, let alone his office been perpetuated by such.
Outside of the absence of manifestation of this Roman papacy in Scripture, even Catholic scholars as well as others provide evidence against the Roman propaganda of such.
Klaus Schatz [Jesuit Father theologian, professor of church history at the St. George’s Philosophical and Theological School in Frankfurt] in his work, “Papal Primacy,” finds,
If one had asked a Christian in the year 100, 200, or even 300 whether the bishop of Rome was the head of all Christians, or whether there was a supreme bishop over all the other bishops and having the last word in questions affecting the whole Church, he or she would certainly have said no." (page 3)
Catholic theologian and a Jesuit priest Francis Sullivan, in his work From Apostles to Bishops (New York: The Newman Press), examines possible mentions of “succession” from the first three centuries, and concludes from that study that,
I stand with the majority of scholars who agree that one does not find evidence in the New Testament to support the theory that the apostles or their coworkers left [just] one person as “bishop” in charge of each local church...
As the reader will recall, I have expressed agreement with the consensus of scholars that available evidence indicates that the church of Rome was led by a college of presbyters, rather than a single bishop, for at least several decades of the second century... — Francis Sullivan, in his work From Apostles to Bishops , pp. 221,222.