"And since the gates of hell trying, if they can, to overthrow the Church, make their assault with a hatred that increases day by day against its divinely laid foundation, we judge it necessary, with the approbation of the Sacred Council, and for the protection, defense and growth of the Catholic flock, to propound the doctrine concerning the 1. institution, 2. permanence and 3. nature of the sacred and apostolic primacy, upon which the strength and coherence of the whole Church depends." Pastor Aeternus, introduction, paragraph 6.
Pope Francis (and his theologians) appears to disagree with that solemnly defined nature and mission of the Church and of the papacy, but his disagreement, since not ex cathedra, is not infallible. On this he is clearly wrong (regardless of everything else he might have right).
More on Vatican I and the extent and limits of papal infallibility later.
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