Your response - That difference in meaning doesn’t really exist in the Greek spoken at the time of Christ. But in any case, as John 1:43 shows, Jesus named Peter “Cephas” in Aramaic, which is the exact same word as “Rock.” In Aramaic it’s Cephas and cephas; literally translating that to Greek would give you Petra and petra, which is a problem, since Petra is feminine, and can’t be used as a man’s name. So St. Matthew renders it as the male Petros instead.
Perhaps St. Matthew rendered it that way to prevent the exact reading you're trying to argue. The masculine form, Petros, applies clearly to Peter. If the second reference applies to the statement of faith, using the feminine form, Petra, aligns with the feminine gender of faith. Why would Matthew mix genders if both refer to Peter?
Because that is the way it is done in the Greek. They have their own rules of grammar and do not translate easily into English. If Jesus had truly meant to refer to him as a "small stone" there is a perfectly good word, "lithos."
Further in John 1:42 Jesus refers to Peter as Kephas/ Cephas. In the Aramaic this means rock any way you slice it.