The later Wittgenstein advanced a revolutionary but puzzling conception of how philosophy ought to be practised: Philosophical problems are not to be coped with by establishing substantive claims or devising explanations or theories. Instead, philosophical questions ought to be treated ‘like an illness’. Even though this ‘non-cognitivism’ about philosophy has become a focus of debate, the specifically ‘therapeutic’ aims and ‘non-theoretical’ methods constitutive of it remain ill understood. They are motivated by Wittgenstein’s view that the problems he addresses result from misinterpretation, driven by ‘urges to misunderstand’. The present paper clarifies this neglected concept and analyses how such ‘urges’ give rise to pseudo-problems of one particular, hitherto little understood, kind. This will reveal ‘therapeutic’ aims reasonable and ‘non-theoretical’ methods necessary, in one clearly delineated and important part of philosophy. I.e.: By developing a novel account of nature and genesis of one important class of philosophical problems, the paper explains and vindicates a revolutionary reorientation of philosophical work, at the level of both aims and methods.