This paper analyzes the ASPIC+ argumentation system. It shows that it is grounded on two monotonic logics which are not Tarskian ones. Moreover, the system suffers from five main problems: i) its logical formalism is ill-defined, ii) it may return undesirable results, iii) it builds on some counter-intuitive assumptions, iv) it violates some rationality postulates, and v) it allows counterintui...