We present a new model of nonmonotonic inheritance based on dialectical argumentation over mixed inheritance networks. A mixed inheritance network consists of strict and default links between nodes representing classes of objects. An object is represented by strict or default connections to nodes of an inheritance network. Rules for constructing allowable arguments are presented. A defeat relation between argument pairs is defined in terms of argument strengths. We represent the vulnerability of elements of the defeat relation to impacts from other arguments. Notions of defendable and justifiable arguments are developed. A flexible decision procedure for determining acceptability of an inheritance claim is defined in terms of burden of proof. We apply our model to examples from the inheritance reasoning literature, demonstrating its key properties. An appendix demonstrates our Scheme implementation on further examples.