When agents communicate, they do not necessarily use the same vocabulary or ontology. For them to interact successfully, they must find correspondences (mappings) between the terms used in their respective ontologies. While many proposals for matching two agent ontologies have been presented in the literature, the resulting alignment may not be satisfactory to both agents, and thus may necessitate additional negotiation to identify a mutually agreeable set of correspondences. We propose an approach for supporting the creation and exchange of different arguments, that support or reject possible correspondences. Each agent can decide, according to its preferences, whether to accept or refuse a candidate correspondence. The proposed framework considers arguments and propositions that are specific to the matching task and are based on the ontology semantics. This argumentation framework relies on a formal argument manipulation schema and on an encoding of the agents' preferences between particular kinds of arguments. Whilst the former does not vary between agents, the latter depends on the interests of each agent. Thus, this approach distinguishes clearly between alignment rationales which are valid for all agents and those specific to a particular agent.