1. A Little History
2. The Authority of God
3. Different Kinds of Speaking
We mentioned in the introduction that God does different things in Scripture. Scripture tells stories about Israel, Christ, and the church. It expresses feelings. It gives laws to Israel. It gives wisdom. It indicts Israel of faithlessness. It predicts and promises. It guides the church.
Many Christians do not take these genre differences into account when they are appropriating Scripture in their lives. For example, many read the Bible as a set of lessons to learn. I learn something from a story. I learn something from a command. I learn something from a letter. No doubt it is completely true that we can learn something from every part of Scripture.
There are also some assumptions to this use of Scripture. This way of using Scripture is very "head" oriented. It views Scripture primarily as a tool to learn things with our heads. It often uses Scripture to create a list of things to believe. As one person has pointed out, this way of using Scripture does not actually guarantee that your life actually changes, which would be a most unwesleyan use of Scripture indeed. 
While we should be open to anything God wants to teach us through the Bible, we cannot fault those who listen more carefully to the genres or types of literature in the Bible. For example, when Paul says, "I wish they would go the whole way and emasculate themselves!" (Gal. 5:12), he is not teaching something to learn. He is expressing strong displeasure with his opponents in Galatia.
Can we learn something from his frustration? Sure. It's okay for Christians to get angry. But that's not the point. That's not what Paul was doing here. The same applies to the psalmist's expression in Psalm 137: "Happy is the one who seizes your infants and dashes them against the rocks." The point was not to teach something, to assert something. That's just not the genre of this verse. It is an expression of emotion.
So for those who read verses like these for what they actually were intended to mean, it is not a little strange to try to apply the word "inerrancy" to them. To say something is inerrant would most naturally mean to say that an assertion is true. But verses like these are not making assertions. They are expressing emotional frustration. We can draw assertions from these expressions, but that was not the point. Those are secondary reflections, not the primary meaning.
It is this sort of deeper reflection on the nature of varied biblical genres that led Kevin Vanhoozer to say that the fundamental category should be that of infallibility. Scripture does not fail to accomplish the purposes that God sets out for it to do. These purposes were originally varied, and it is the task of the biblical expert to identify what these original purposes were.
It is also important to point out that this use of the word "infallibility" is different from the way the word was used in earlier debates. In the debates of the 70s, some groups used the word "infallible" to restrict the Bible's authority to matters of salvation, faith, and practice. In other words, they used the word to say that the Bible may not be accurate in matters of science or history. This is not how we--or Vanhoozer--is using the word.
We are rather using the word in the sense that something does not fail. This moves us to the question of purpose. What exactly was God trying to do through a particular passage? It may very well be that God was not trying to assert historical detail or scientific precision in a passage. And of course if it was not God's purpose to do so, then he certainly did not fail.
Inerrancy is thus seen to be a subcategory of infallibility. When it is God's purpose to assert some truth, that truth will be without error. God does other things through Scripture. He makes promises, for example. When God promises that Christ will return some day, that promise will not fail. It will indeed take place. But the purpose of a promise is not primarily to assert a truth.
God also makes commands through Scripture. These commands are authoritative. In this case, the word "authoritative" seems more helpful than either the words "infallible" or "inerrant." God allows people to disobey his commands, so a command does not guarantee it will happen--at least not when we are talking about commands God allows us to disobey. So here the word "authoritative" is the better fit.
The point is that it is perfectly acceptable for Wesleyans to be more sophisticated in the way they use words like "authoritative," "infallible," and "inerrant." When God makes a command, it is authoritative. When God does something else through Scripture, his purpose will not fail and it is "infallible." When that purpose is to assert a truth, then the assertion is "inerrant."
Sometimes, God's purpose may be simply to allow a biblical author to express frustration, as in the verses above, to where he is neither commanding or asserting anything. Sometimes God allowed the biblical authors to use acrostics or poetic artistry, whose point was not to teach or do anything but express beauty. We can certainly learn something from these expressions, but that was not the point.