Yes, it is. Perhaps not in everything, since some parts of the moral law or other aspects of Scripture are quite simple and perfectly plain. But not everything is, and St. Peter warns against the presumption, as one finds in 2 Peter 3:16. Scripture, then, is not as "perspicuous" as some allege. Yet, regardless, it is both inspired and infallible. To that end, its infallibility is only rendered useful in the "difficult" cases, through the agency of an infallible authority. Since Jesus Himself does not instruct each of us personally, that authority is through a human agency that He established, as Scripture makes clear enough in the passages I cited earlier. That agency is the Church. Specifically, that Church which has existed throughout the entire span of the Christian Era, and has kept the Deposit of Faith delivered to it from the Apostles, through the working of the Holy Spirit. There is only one such Church that can claim both the historic continuity required and the intact Deposit of Faith at issue.
That church — Christ’s church — is the Christian church, not the Catholic church. It is my church, and your church. As believers and followers of Christ, we can both rightly claim to be members of the body of Christ.
Like I said, lineage doesn’t make a difference to me, as we both trace the origin of our faith to the same point. We divided, but our origins and lineage are the same to the point of division. One can dispute, I suppose, whether the division was a heresy or a divinely inspired separation ... but I would claim the latter.
I cannot believe in the infallibility of any human being or human organization, as it conflicts with the established doctrine of original sin. Humans are inherently fallible, and no Biblical passage gives me reason to believe that any infallibility rests in a man or a hierarchy. Such would be putting faith in a man or group of men rather than the Almighty.