Every belief structure can be thought of as a map. Our observational experience is akin to the actual terrain. For whatever reason, most people of faith are not very apt at comparing their map to the surrounding terrain. Any difference in the two is contradiction.
Modern Mormons suppress contradictions to their model, but they aren't alone in the practice. This behavior is the result of confirmation bias or cognitive dissonance. Confirmation bias occurs when we see all evidence as support for what we already believe when some of it is actually evidence that opposes what we believe. Cognitive dissonance is a negative emotive response that occurs when our experiences contradict our belief system, causing us to flee from or ignore situations that do not support our belief system. We see examples of these phenomena not only in the way we selectively remember things, but also in the way we interpret evidence. This is why one scripture can be read that directly contradicts a tenet of someone’s faith, yet that person can contort it to fit.
It only takes a single contradiction or counterexample to prove an idea false. For instance, if I said all pigs fly, I would only need to find one pig that did not, in fact, fly, to show that all pigs do not fly. For a scriptural example, look at Sherem. He said that no man can know of things future, but also said that there should be no Christ, which he couldn’t possibly know unless men could know of things future (see Alma 30). Contradictions can be a powerful tool for discerning between truth and error.