Here's an old post I made to someone else months ago:
I think there is even another explanation worthy of consideration here.
Others who have covered the topic explain how Peter was actually referred to as a small rock. These verses confirm what Jesus was saying:
1Pe 2:4; To whom coming, [as unto] a living stone, disallowed indeed of men, but chosen of God, [and] precious,
1Pe 2:5; Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ.
Look who is teaching here . . . none other that Peter, himself. Whats he teaching on? Could it be on what Christ taught to the twelve in Matt 16? As many argue, we as individual members together comprise Christ's church; as lively stones we build up His spiritual house.
Notice how Peter addresses himself at the beginning of this teaching:
1Pe 1:1; Peter, an apostle to Jesus Christ, to the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia,
He refers to himself as an apostle of Jesus, not as the chief apostle, not even as first among equals. Peter, too, was a lively stone.
When Jesus spoke to Peter in Matt 16:18, it was to address Peter's response to the question Jesus had just asked of all twelve, "who do ye say that I am." He spoke directly to Peter in this instance, because it was Peter who stepped forward and answered Jesus' question. We, who have all been students at some point in our lives, can envision how this occurred.
Remember sitting in the class room, the teacher is lecturing on a subject and asks the whole class a question. Usually, one student responds, and when this student does so, then teacher then invariably (if just for a moment) focuses his attention on that student and his response.
This is what happens with Jesus and Peter here, Peter steps forward like an enthusiastic student who wants to impress his teacher. So, for just a moment Jesus attention is on Peter. Yes, Jesus responds to Peter, Matt 16:17; And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed [it] unto thee, but my Father which is in heaven. Matt 16:18; And I say also unto thee, That thou art Peter, and upon this rock I will build my church . . . . .
In essence Hes saying, thou are a rock/pebble/stone . . . . then, he continues upon this rock, we can infer that the second rock referenced is not Peter by the usage of the word this. This rock is arguably Peters declaration of Jesus identity, or you know were missing possible hand gestures Jesus may have been making. He could have point to Himself, he could have passed his hand over all twelve of the apostles, or made a wide, sweeping hand gesture encompassing the earth . . . we just were not there to know.