Unsupervised visible-infrared person re-identification (USVI-ReID) aims to match specified persons in infrared images to visible images without annotations, and vice versa. USVI-ReID is a challenging yet underexplored task. Most existing methods address the USVI-ReID through cluster-based contrastive learning, which simply employs the cluster center to represent an individual. However, the cluster center primarily focuses on commonality, overlooking divergence and variety. To address the problem, we propose a Progressive Contrastive Learning with Hard and Dynamic Prototypes for USVI-ReID. In brief, we generate the hard prototype by selecting the sample with the maximum distance from the cluster center. We reveal that the inclusion of the hard prototype in contrastive loss helps to emphasize divergence. Additionally, instead of rigidly aligning query images to a specific prototype, we generate the dynamic prototype by randomly picking samples within a cluster. The dynamic prototype is used to encourage variety. Finally, we introduce a progressive learning strategy to gradually shift the model's attention towards divergence and variety, avoiding cluster deterioration. Extensive experiments conducted on the publicly available SYSU-MM01 and RegDB datasets validate the effectiveness of the proposed method.