Human–AI collaboration in knowledge-intensive tasks such as fact-checking requires understanding model uncertainty in multi-document reasoning amid conflicting/agreeing evidence. Yet, existing methods only express uncertainty as numbers or hedges without revealing which evidence conflicts cause the uncertainty, leaving users unable to resolve disagreements. We present CLUE (**C**onflict- Agreement-aware **L**anguage-model **U**ncertainty **E**xplanations), a plug-and-play white-box framework that, to our knowledge, is the first to generate natural-language explanations of model uncertainty grounded in conflicting/agreeing evidence. CLUE (i) identifies span-level claim–evidence and inter-evidence relations that signal conflict or agreement without supervision, and (ii) uses these relations to steer explanation generation, articulating how they drive the model’s uncertainty. Across three language models and two fact-checking datasets, CLUE produces explanations that more faithfully track model uncertainty and better align with the model’s fact-checking decisions than span-agnostic explanation prompting; human raters also judge them more helpful, more informative, less redundant, and more logically consistent with the input. By explicitly tying uncertainty to evidence conflicts and agreements, CLUE supports practical fact-checking and other tasks that require reasoning over complex, conflicting information.