Yet it could translate that way: "Thou art Rock and upon this Rock..." would be an equivalent translation.
The problem with English is that Rock is almost never used as a male given name (except for Rock Hudson I can't think of one--- and the translations were done pre-Rock Hudson!); but in languages were the word "Rock" is a given name, that's how they translate the whole verse consistently. Check it out:
FRENCH(Iscool)"If they meant the same thing, Jesus would have used the same word for both rocks..."18 Et moi, je te déclare: Tu es Pierre, et sur cette pierre j'édifierai mon Eglise...
HILIGAYANG/Filipino
18 Kag tungod sini ginatawag ko ikaw nga kon sayuron bato. Kag sa sini nga bato pagatukuron ko ang akon iglesya,
ITALIAN
18 Tu sei Pietro e su questa pietra costruirò la mia Chiesa; e tutte le potenze dellinferno non potranno vincerla mai.
(Pietro and pietra are masc. and fem. of the same word)
RUSSIAN
18 И Я говорю тебе: ты скала, и на этой скале Я построю вселенскую общину Моих последователей,
(скала and скале are masc. and fem. of the same word)
PORTUGUESE
18 Pois também eu te digo que tu és Pedro e sobre esta pedra edificarei a minha igreja,
(Pedro and pedra are masc. and fem. of the same word.
But He did:
GREEK
18 καγω δε σοι λεγω οτι συ ει πετρος και επι ταυτη τη πετρα οικοδομησω μου την εκκλησιαν και πυλαι αδου ου κατισχυσουσιν αυτης
(πετρος and πετρα are masc. and fem. of the same word)
You say: "It is foolish to claim Jesus used two different words that mean the same thing in the same sentence..." ... but the fact is, Jesus DID use the same word, and it is foolish to claim he would use the same word twice, in the same sentence, to mean different things.
The Catholic Church Fathers said that the different gender was due to the Petra being the profession by Peter, whereas the Petros was to designate the man, Peter.
To make the profession establishes a foundation so solid that no one can snatch us from God's hand (to mix two metaphors). The Holy Spirit inspired the use of the masculine and then the feminine so there would be no mistake that it is a foundational thing at issue. Then Jesus immediately gives Peter the keys to the Kingdom.
And every time someone makes that same profession and believes God raised Him from the dead as their Savior, they are added to the 'thing being constructed' during the Church Age 'pause' in the 490 years assigned for God dealing with the Jews specifically. Thus the Church, the Ekklesiaa of believers, is being constructed upon a foundation which Peter illustrated with his profession, and this did not flee from him even though he denied Jesus thrice just a few days later! Peter was added into the construction project upon professing, and since he was the first added, he was given the keys to open the Church Age at Pentecost.
Actually that is not true. Eastern dialects and Aramaic idioms would employ such usages to make a point or a pun. In this case Jesus was contrasting the smaller shakier rock of Peter with Himself - The Rock. The Apostles and anyone else at that era would have understood and enjoyed construction of that sentence.
Is it possible?
That is complete nonsense...