Work in the mental model tradition has shown that human reasoners are subject to fallacious inferences from very simple premises that have been described as tantamount to cognitive illusions. We present four experiments that show that these phenomena are much more general and systematic than has previously been thought. Among other results, we find that premises using `some' mirror premises using `or' in generating fallacious inferences, showing that there are interesting facts about reasoning with quantifiers beyond syllogisms that have been the main focus in the literature. Neither mental model theory nor other familiar theories of reasoning account for the results we present. However, the novel illusory inferences we present are predicted by the erotetic theory of reasoning (Koralus and Mascarenhas, 2013). The key idea is that, by default, we reason by interpreting successive premises as questions and maximally strong answers to those questions, which generates the observed fallacies.