The truth is the exact opposite interpretations should apply - here’s why we know that for sure.
When Jesus gave the keys to Peter in Matthew 16:19, he says "
“I will give you the keys of the kingdom of heaven; and whatever you bind on earth shall have been bound in heaven, and whatever you loose on earth shall have been loosed in heaven.”
Jesus then extends those same keys to ALL of the disciples when in chapter 18 he says, “Truly I say to you, whatever you bind on earth shall have been bound in heaven; and whatever you loose on earth shall have been loosed in heaven.”
Another major confirmation that Peter isn’t the only one the church is built upon comes from Ephesians 2:20 when Paul says, “So then you are no longer strangers and aliens, but you are fellow citizens with the saints, and are of God’s household, having been built on the foundation of the apostles and prophets, Christ Jesus Himself being the corner stone, in whom the whole building, being fitted together, is growing into a holy temple in the Lord, in whom you also are being built together into a dwelling of God in the Spirit.” Note that the foundation is ALL of the apostles and prophets, not just Peter. The only individual singled out for special recognition is the chief cornerstone, which is Jesus, as he should be.
No other proof is needed to know that Peter, while first among equals, is not the sole rock upon which the church is built. He was simply the first among those who were recognized. ALL of the apostles AND prophets share equal weight as the foundation of the Church. Scripture can’t be more clear on this.
As for John representing the Church, that’s not consistent with what actually followed. Jesus was doing a very practical thing. His love for his mother led him to place her into his beloved disciples care for the remainder of her life. Tradition holds that John took her in and cared for her 'til her death.
David