The "rock" is not Peter. Yeshua used the word "petros" when referring to Simon Peter. It means "little movable pebble." He used the word "petra" to refer to Himself (or to Peter's confession). It means "large immovable boulder." Our faith is based on the solid Rock of Yeshua...not on a little human pebble or stone.
During a discussion of the Democrat party, a pundit...after pointing out that God was voted down three times at their convention...might say: "This is the modern Democrat party." Of course, the word "is" in that sentence should not be taken literally. Instead, it means "represents." Likewise, Yeshua was using a common idiom when He said "take, eat; this is (i.e. represents) my body/blood."