This paper draws on Euripides’ Alcestis to propose a new way of approaching the tragic agōn. It reads the debate scene of that play not as a rhetorical showpiece but as a piece of dialogue and an interaction that follows the principles of communicative pragmatics. In this interpretation Admetus and Pheres do not aim to persuade each other about whether it would have been right for Pheres to sacrifice his life for his son; instead, father and son are engaged in redefining their relationship, at the same time hurting each other as much as possible. Therefore, analyses that focus on ethical arguments concerning Pheres’ refusal to die and on how they reflect on the two persons' characters fail to capture an essential aspect of the quarrel. If, however, the communicative nature of the agōn is taken into consideration, illogical and seemingly idiosyncratic passages of the speeches can be explained as functional, and its transformed purpose chimes with Euripides’ rearrangement of the traditional myth, as he places the debate after Alcestis’ death.