Evangelicals and Fundamentalists commonly say the Bible is infallible. I wish they would stop. It is a misconstrual of the word. I know they mean well, but they are abusing a good and useful theological term.
Fallible means able to make a mistake or able to teach error. Infallible means the opposite: the inability to make a mistake or to teach error.
When we use these words, we use them regarding an active agent—that is, we use them about someone making a decision that either may or may not be erroneous (in which case that someone is fallible) or that definitely cannot be erroneous (in which case that someone is infallible).
Put another way, the active agent is alive and capable of making decisions. A human being is an active agent. Normally human beings are fallible. Sometimes they decide rightly, and sometimes they decide wrongly. In a few instances (such as the pope when speaking ex cathedra or the bishops united with the pope when speaking through an ecumenical council) human beings may decide infallibly.
But a rock is never infallible. Nor is it fallible. It is neither because it makes no decision about anything. Ditto for a plant. No sunflower ever made the right decision—or the wrong decision. In fact, no sunflower ever made any decision, properly speaking.
The same can be said of a book. No book, not even the Bible, is capable of making a decision. This means it would be wrong to say that the Bible is either infallible or fallible—such terms should not be used about it or about any other book.
The proper term to use, when we are saying that the Bible contains no error, is inerrant. In its teaching, a particular book may contain truth or may contain error; most likely it will teach some of each. The one exception is the Bible. The Church teaches that everything the Bible asserts (properly understood, of course) is true and therefore without error.
Inerrant would not be the word to use about, say, a pope. A pope may act infallibly in carefully prescribed circumstances, but he is not inerrant. To claim that he is inerrant is to claim that he "contains" no error, but every pope does. A pope’s store of knowledge, at least on matters of religion, is likely far better than yours or mine, but no pope has had a mind so capacious and exacting that he knew every religious fact with perfection.
When Vatican I (1869–70) taught about papal prerogatives, it did not say that the pope is inerrant. It said he teaches infallibly in certain circumstances. He is able to do that through the superintendence of the Holy Spirit.
Like other disciplines, theology has words of art. For them to convey their true meaning, we must use them accurately. We need to understand that the Bible is inerrant and the pope infallible—but not the other way around.