If the acknowledged headship of Peter -- as the Coryphaeus, the Mouth, the Chief, the Keyholder -- of the Apostles did not detract from or negate the authority of the original Apostles, how can or does the Pope's authority, *as Peter's successor*, detract from or negate the authority of local bishops?
It's crucial to keep the Pope in the Church. He's not some bizarre action figure stapled onto Christian history and tradition. We can't talk about him or his role *outside of the Church*. And the Church is infallible. In my eyes, the Pope's "personal infallibility" (already a skewed formulation of papal infallibility) is but the concrete, incarnational consequence of an infallible Church that speaks for God. The Church is the Body of Christ; and every body has a mouth -- especially an infallible one.
Protestants claim the Bible is infallible, which is true. But how is the Bible infallible *in concrete life*? All Orthodox, Catholics and honest classical Protestants admit the Bible is infallible *only as declared by and from the Church*. A problem, however, arises when we agree with Orthodox and Catholics that *the Church also is infallible*. But again, in conrete human terms, how? How is the Church infallible? The Church is infallible as She speaks the truth of God *with one voice, as one Body*. It just so happens that speaking with one voice means a person with one voice speaking. Such is life. I find it very helpful to stop calling the Pope "the Pope /gasp!/" and instead regard him as but the logical result of an infallible *speaking* Church. As Nemwman said, ecclesial infallibility is a consequence of biblical inspiration. Likewise, papal infallibility is a consequence of ecclesial infallibility.