If you don't make mistakes and you're never wrong, you can claim infallibility. (You're going to have to own up to self-deception, too, because, well, humans make mistakes.)
If you're convinced of the infallibility of your sense of direction, you won't worry at all when you're deep in the dark woods at night and your flashlight dies. Maybe you’ll get out of the woods, but human infallibility usually doesn’t last. You may buy into your economics professor's image of infallibility until he comes to class with mismatched socks and toothpaste on his forehead. Infallibility comes from the Latin fallere, "deceive," and with infallibility, you can't be deceived.