Why a single lucky — or unlucky — split of your data can hand you a performance number that's technically correct and still deeply misleading.
Every model needs to be evaluated on data it wasn't trained on — that part isn't in dispute. The question this page is actually about is subtler: how much should you trust the one performance number that evaluation produces? A simple train/test split gives you exactly one number, from exactly one arrangement of which rows ended up on which side. K-fold cross-validation gives you several numbers, from several different arrangements, and — critically — lets you see how much those numbers agree with each other. That second thing, the agreement (or disagreement) across folds, is information a single split can never give you at all.