Start with the concession the objector is owed: the word “infallibility” appears nowhere in Scripture, and no verse describes a Roman bishop defining doctrine without error. The Catholic case is built by inference — and the same texts are read more modestly by the Orthodox, who grant Peter a primacy without the papal charism, and by Protestants, who grant neither. The verses, on their own, underdetermine the dogma. A Catholic who pretends Luke 22 simply says “papal infallibility” is not reading carefully.

But the texts are not nothing, and they point somewhere. In Luke 22, Satan demands to sift the apostles — the “you” is plural — yet Christ’s prayer narrows to one man: “I have prayed for thee, that thy faith fail not: and thou, being once converted, confirm thy brethren.” A faith-preserving prayer for one, ordered to the strengthening of the rest. That is not a private comfort; it is a stabilizing office. (Honesty names the gap the objector presses: the verse’s own setting is Peter’s coming fall and recovery, and it says nothing of successors — the step from Peter to the Bishop of Rome is the disputed move, and it is not in Luke 22 itself.)

It joins the other Petrine texts. Peter alone is given the rock and the keys, and is the first to whom the power of binding and loosing is entrusted — a power later extended to all the apostles (Matthew 18) — under the promise that “the gates of hell shall not prevail” (Matthew 16); Peter alone is told “feed my sheep” over the whole flock (John 21). And these rest on the Church’s own indefectibility: the Spirit will guide her “into all truth” (John 16), and she is “the pillar and ground of the truth” (1 Timothy 3:15) — a promise to the Church, which the Orthodox affirm no less, locating it in the council rather than the pope. The Catholic adds the second, disputed premise: that Peter is the Church’s divinely-set point of confirmation. Grant both, and the infallibility of the Petrine office in its solemn definitions is the coherent unfolding of the whole — not a proof-text, but a development.

And it is precisely scoped. The doctrine does not say the pope is sinless, inspired, or generally right — only that when he defines, ex cathedra, a matter of faith or morals for the whole Church, he is preserved from error. That is a narrow and intelligible claim, drawn from Scripture read with the Church rather than against her. The honest summary: the term is not biblical; the doctrine is biblically rooted, and grows.