It's not an appeal to authority. I am just presenting Lewis's take on the matter, one that I agree with in point of fact, and which I believe I can defend. The idea that you can somehow theologically to Scripture as a blank slate to be written on with no presuppositions or questions of one's own is alien to my way of thinking, and quite implausible based on my understanding of epistemology.
The trouble is that Scripture only indirectly addresses the problems that we are interested in. In Romans 9, for example, Paul is concerned not about the election of individuals but in explaining the unbelief of Israel and explaining how God's promises were not broken.
What you get in Scripture are some strands emphasizing sovereignty, some emphasizing personal responsiblity, and strands emphasizing the universality of love. So what people do is extrapolate. Strictly speaking Scripture can't answer the question of predestination as you and I would ask it, because it doesn't ask the question. I can extrapolate in ways that require me to set aside my strongest moral convictions (I don't even like saying intuitions here) or I can avail myself of extrapolations that don't require abandoning what I take to be very basic moral convictions.
Scripture doesn't even begin to function authoritatively unless a person thinks there is a omnipotent, omniscient and perfectly good being. Since God by definition is a being who is omniscient, omnipotent, and perfectly good, what that means is that, at least logically, we have to know how to use the word "good" before we could possibly know how to use the word "God." And Scripture doesn't get its authority until we have the conviction that it comes from God, which we would not be able to recognize even if we had a pre-existing conception of "good."
What I am more or less a skeptic about is the extent to which we can get the precise meaning out of Scripture via historical-grammatical analyses. I don't believe that final doctrinal answers can be read off these kinds of analyses. They are very helpful, but they are quite human attempts to put me inside the mind of people 20 centuries distant from me who spoke a language I don't speak. Further, exegetes seem to me to reflect the theological biases they bring to the text.
Then we have to look closely at the kind of inerrancy we are dealing with. Scripture passages would have led people in OT times to believe that righteous conduct results in earthly reward and wicked conduct results in earthly punishment. Passages in, for example Deuteronomy, would strongly lead us to think that. That's probably was the comforters of Job had in mind. I am sure they were the best exegetes in town. They just got it wrong.