He's talking about the problem of authority as in: who has it.
You are completely wrong about where we place our faith. Protestantism places its faith in scripture, their confession says so. But this is on the face a novel approach, because no such system could have been instituted by the Apostles. Therefore this is not the faith of the Apostles.
We don't place our faith in the writings and interpretations of Christians who have gone before us. This is not true. We don't place faith in the Fathers. We place our faith in Christ, solely in Christ. In Him, through "His precious and magnificent promises" we receive the truth. One of these promises is that of the Church. Our faith requires belief in the Church, because we are baptized into Christ and in doing so become members of His Body. Christ is One, His Body is One, therefore the Church is One.
Let me make this clear - the chain is:
Christ -> Church founded on Apostles and Prophets -> Apostolic Tradition -> Holy Scripture
Or, working backwards, we can say we can trust Holy Scripture because it aligns with Apostolic Tradition, which comes from the Apostles, on whom the Church was founded by Christ.
Protestants have something like:
Christ -> ??? -> The Bible
Working backwards, they say we believe in the Bible because of Christ. But there's a huge swath of history in the ??? because the Bible as they know it today didn't exist for over a thousand years. They say that's ok because reasons.
Protestants have no such bedrock chain of authority. They're left with a book as the ultimate authoritative entity. Unfortunately, when asked by what authority this book exists they must necessarily stand mute; they have no ability to go "before the book" even though we know temporally this time was a necessity. They have no ability to go "outside the book" to understand why the canon is what it is, why books were included or rejected, and on what grounds. They're left with a book and no one to explain it to them. And so there are so many errors that creep in. And since a book can't tell you if you're right or wrong in reading it, they end up being subject to the interpretation of those "fallible men" they are so afraid of in the first place (even if those fallible men are themselves).
Quote:
Protestants see great value, but they also see the fallibility of man, of the Catholic Church throughout history, and place inerrancy solely on the Word of God.
The Catholic (universal) Church is not fallible. It is the Body of Christ, in submission to Christ, spotless and undefiled, and He is the Head. The Scripture says this much. If you believe the scripture is inerrant, you must believe the Church to be unconquerable.
As for submitting to the authority of God, you can't have it both ways. You said you submit to scripture - is the scripture God? The scripture says to submit to spiritual authorities and to each other as to Christ - are spiritual authorities God?
You must have a hierarchy of authority to understand who to submit to. This is scriptural. Lacking this, protestants unintentionally enter into a problem of very great hubris, as you quote says - I submit to no man, only God Himself! Thus making yourself the only spiritual authority. Isn't that what you were saying you didn't do?