From a Wittgensteinian point of view, my goal is to argue against the idea that teaching critical thinking should have as one of its aims the possibility of changing or adapting our deeply held beliefs. As pointed out by the Austrian philosopher in On Certainty, we have a world-picture which is neither true nor false, but above all, 'it is the substratum of all my enquiring and asserting' (OC, §162). Besides that, in his remarks on Frazer's Golden Bough, Wittgenstein insists on the idea that different communities have their own rituals that express ways of acting, which become crystallized in their customs and institutions, similar to the magical rituals described by Frazer. The degree of similarity among them is greater than we suspect, and what interested Wittgenstein was to understand how we see things by looking for the links between the various ritualistic events. Based on these remarks, I argue that, if our deeply held beliefs are a source of necessity, instead of aiming to change/adapt them, teaching critical thinking should--by showing the links between diverse cultures--essentially avoid employing them in a dogmatic way, since our own deeply held beliefs could have been different ones.