The Bible as "inerrant" – as distinct from authoritative: New Frontiers preaching

I struggle with the concept of “inerrancy” – any schoolboy can find errors in Scripture. Where does Cain’s wife come from?

A preacher from New Frontiers International argues that the church is founded on the basis of the new testament – but this is nonsense. The New Testament is itself a creation of the church at the Council of Nicea in 326A.D. I wonder if he and others of his ilk have trouble with this kind of plain history, and only see modern house churches like NFI as the “true church”.