Well said.Yes, Peter's name means a small stone or pebble. And Jesus is the rock. So Jesus is telling Peter that he is just a small stone and the church will be built on the rock of Jesus. Notice Jesus never told Peter that the church would be built on "you". He said, Peter you are a little stone and the church will be built on me ( the rock). Any church that has a human for it's foundation is not God's church. God's church is built on the foundation rock of Jesus.
The first 64 men listed by Rome as a succession of popes never made any such claim for themselves; nor were they in any sense ever regarded as Universal Patriarchs and heads of the church; on the contrary, both they and their associates repudiated such a pontifical office as anti-scriptural and anti-canon.
Prior to the year 606 A. D. there never was a church in Rome regarded as "mother", nor a Bishop regarded as the head of the universal church..”
“The Pope's Claim To Authority - No. 3” by W. Wallace Layton, April 13, 1950 issue of Gospel Guardian.