I'm afraid your author doesn't really understand Greek grammar, or else he is running one of his rabbit trails (Bullinger had a burr under his saddle about a number of theological issues.) In this case, looking for the nearest feminine noun (in another sentence) is not a sound grammatical argument. Greek nouns don't have to agree in gender in a parallel construction - think! otherwise you could only place in parallel nouns which happened to be of the same gender. And gender (other than obvious things like men and women) is random in Greek and not always what you would expect.
Moreover, Christ could not call Peter a feminine name, which would create all sorts of other interpretive problems. One of the goofier contemporary translations tried to express this grammar by saying "You're Rocky - "
Christ wasn't calling Peter a feminine name. Christ was referring to the Church in the feminine.