I gave you the foundational scripture in #580.
While the bishops answer to Christ individually, the Church they build is givern infallibility institutionally. See Mt 16:18.
The rock upon which Christ's church was founded is the individual link with the Father and His guidance, inspiration and motivation. And Jesus lauded Peter for using that relationship to receive the revelation the Jesus was the Son of God.
For, that is a rock.
You can take millions of atoms out of a rock and it still is the foundation of a rock, because all the others bear up the whole weight equally.
If you build salvation of all on a one atom rock, like one all powerful church with exclusive keys to the Kingdom, when that one atom is taken out so does what it holds up crash down.
Of the two rocks, it is the former that the gates of hell shall not prevail against.
Individuals, not corporate entities, please.