In this paper we are interested in the use of argumentation for handling inconsistency in inconsistent knowledge bases expressed with existential rules. We propose an instantiation of an argumentation framework and demonstrate it is coherent, relatively grounded and non-trivial, therefore satisfying the rationality postulates from the literature. We demonstrate how argumentation semantics relate to the state of the art of handling inconsistency in this setting, allowing us to propose the first dialectical proof in the literature for a given semantics.