My faith in the Church rests solely on my faith in Jesus Christ! When Jesus came, one of the things He did was build a Church (Matt 16:16-19). He didn’t say “churches”, but “church”, singular. The Catholic Church is the only claimant to that title. This “Church would exist till the end of time, would never teach error for “the gates of Hell will not prevail against it”. If Hell did prevail against it, then it could no longer be called Christ’s Church. You claim it has fallen into error, while I trust in Him and His promise. As He guaranteed that the human authors of Scripture were free from error when they wrote, so too can He prevent certain individuals from teaching error in their capacity to shepherd His people (see John 21:15-17)
The first thing of note is why would Jesus build a Church instead of having the Scriptures as the final arbiter. One reason, as has been shown by the sad divisions in Christianity, is Scripture cannot interpret itself. An infallible document is ineffective without an infallible interpreter. Even our Constitution needs an interpreter (unfortunately, as has been seen recently, they aren’t infallible)
Another reason would be the fact that most people in early Christianity were illiterate, thus a Sola Scriptura approach would have been, well, laughable since most could not read the “Scriptura.”
Third, even if you can read, do we really understand all the idioms and figures of speech? How do we know that Mark wrote Mark? Mark isn’t even an Apostle, why is he in the canon? How do we know what books belong in the canon? Remember, it was the Catholic Church in 397 that canonized the Scripture as you have it today (well your New Testament, my Old and New Testament). So if you accept her decision on your New Testament canon, how can you reject the same Councils’ decision on Old Testament canon?
Fourth, how about the working mom with six children? Does God expect her, after a hard day at work, after changing the last diaper, after putting the last child to bed, for her to now get out her concordances, Bible dictionaries, lexicons, different translations of Scripture to discern if Jesus is really present in the Holy Eucharist? Of course not! He set up a guide, a sure foundation, so that those who follow her will never be led astray (see Isaiah 35:8) Of course it is God Himself who is the guaranteer that He (God) will keep His Church free from error.
So it is not that we believe that the pope is so smart that he knows it all (though we have been blessed with some awesome men holding that office), but we believe God has his guiding hand on the Church to assure it will faithfully lead His children into heaven.