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Peter is the rock on which Christ built His Church; Peter is the “rock of the Church”. Same thing. No difference. Peter is not THE Church, of course, but He is the rock on which the Church was built.

The complicating little factor there is Peter's own words in I Peter 2. HE considers Christ the stone upon which the church is built. He says nothing about himself.

“rock on...”, “rock of...”, same thing.

Hardly. There's a huge difference between building something *on* a rock and building it *of* rock.

I Peter 2: 4-8 As you come to him, the living Stone—rejected by men but chosen by God and precious to him— you also, like living stones, are being built into a spiritual house to be a holy priesthood, offering spiritual sacrifices acceptable to God through Jesus Christ.

For in Scripture it says:
"See, I lay a stone in Zion, a chosen and precious cornerstone, and the one who trusts in him will never be put to shame."
Now to you who believe, this stone is precious. But to those who do not believe, "The stone the builders rejected has become the capstone," and, "A stone that causes men to stumble and a rock that makes them fall."

They stumble because they disobey the message—which is also what they were destined for.