"upon this rock"; in the greek is petra = bedrock or large stone.
Peter was fallible yet a living stone, which Christ would use as one of the first of many living stones to build his Church. Christ, on the other hand, is that layer of bedrock upon which all living stones are placed in the building of the Church.
Christ is the foundation and it is Christ that is building upon that foundation. Do not err by equating a man as equal to Christ or as Christ's sole representative on earth.
I have. Your misguided, but popular mishandling of the language among reformed Christians is the equivalent, in english, of asserting "butterfly" is related to dairy products.
The discrepancy you make so much of was a linguistic accommodation due to the impropriety of referring to a masculine person with a feminine noun.