Aha, I see.
Mt 16:18 is in part about St. Peter and his primacy, but it also is about Christ’s intention to build His Church which cannot go wrong. So even if for some reason the See of Peter were to go vacant (there are people who are otherwise quite Catholics who believe that), the prophesy about Christ’s Church still stands. Further, St. Peter has the intention to perpetuate his “tablernacle” (2 Peter 1:14-15), and he had the means of Apostolic succession just like any other apostle (see Titus and both Timothys).
The point of the Church being infallible is underscored in how St. Paul calls her the “pillar and ground of truth”. This is, of course, consistent with Jesus being in person the truth.
re 304: I’m not getting into your doctrine with you. I plan on being in Heaven. If you love Christ and get there too, fine by me!