Fine-grained emotion classification (FEC) requires distinguishing subtly different emotions, where the dominant errors come from closely confusable categories. Recent progress relies on contrastive learning with hard-pair mining, implicitly assuming that a fixed similarity metric is sufficient to optimize informative pairs. We argue that this assumption is fragile because defining whether two utterances are similar becomes a problem when the label space is crowded, and hard-pair mining under a fixed metric can systematically miss the worst confusions. Thus, we treat the similarity function as a learnable component and design an adversarial metric learning (AML) framework. It follows theoretical interpretations of metric-robust representations that better separate confusable emotions. AML trains a pairwise discriminator to maximally confuse two targeted hard pair types, while training the encoder to remain discriminative under this worst-case learned metric. Our code and data are released on GitHub.