Counterpossible conditionals are a special kind of conditionals whose antecedents are necessarily false (impossible). There has been a long-standing debate about their nature. According to the supporters of the orthodox view (Lewis, Stalnaker, Williamson and others), they are only trivially or vacuously true. Opponents of the orthodox view (Berto, Jago, Sendłak, Kocurek and others) do not agree with such a position, and according to them, some counterposible conditionals are true (and informative) also in a specific sense. We analyzed some “non-intuitive” arguments of classical logic as precursors to counterpossible conditionals. We demonstrated that these arguments are correct in propositional and predicate logic. Their non-intuitiveness becomes evident only when we accept the tacit assumptions that are imposed by the content of the premises and conclusions. The components of the premises and conclusions of such arguments are enthymemes of other “sub-arguments”, and their non-intuitiveness is based on the factual falsity of the disjunctively connected components of the conclusions as abbreviations of two incorrect arguments. In order to explain the truth of counterfactuals and the validity of the rules of classical logic in this context, it is necessary to assume the validity of the comparative and eliminative principle of ceteris paribus. We used the same methodology for counterpossible conditionals and explained why some conceptual or mathematical counterposesible conditionals are non-trivially true and others are not. It is decided by the acceptance of tacit assumptions that are in accordance with the explicit assumptions, and the validity of the comparative and eliminative principle of ceteris paribus. Finally, we showed why logically counterpossible conditionals cannot be non-trivially true: we cannot support them with other tacit logical truths in order to make them true.