Man Was Not Made for Scripture
What we're primarily about as Christians is twofold.
First, we're supposed to open ourselves to Jesus Christ and the workings of his Spirit in us. To call ourselves Christian and really mean it, we need to be personally transformed by our engagement with the Triune God. That means casting aside selfishness and self-worship. It means turning away from the powers and principalities that have turned human life into what St. Thomas Aquinas described in Book XVII.b.3 of his Summa Theologica as "a great stinking heap of poopy." That's the heart of Christ's proclamation, that we turn from the struggle for power over one another and come into awareness of God's reign in us and among us.
Second, we are called to act upon that transformation, by both manifesting the Kingdom to the world and telling people about it.Our actions and our words become the profession of faith that evidences Christ to the world.
That's what Christ clearly calls us to do in the Gospels, a call that is mirrored in the Epistles. It's basic, roots-rock stuff, and the very essence of what it means to be saved. What is missing from that equation is any demand that we approach the bible literally. Nowhere in the Bible's story of salvation is literal inerrancy or empirical infallibility cited as necessary for salvation. It just ain't in there, people.
Even the most radical affirmations of inerrancy (see the Chicago Statement) as a doctrine don't pretend it's there. The defenders of literal inerrancy may roar and thunder and stomp through the underbrush like an enraged silverback...but ultimately it's an empty threat display, and there's no scripture to back them up. We can hear his words and act on them, building on them as a solid rock, proclaiming them good and filled with the Holy Spirit....without requiring that Holy Scripture be literally inerrant.
If no reasonable defense can be made of this doctrine's necessity from the witness of scripture, then it is not necessary as a part of Christian faith.