Accurate prediction of metro Origin-Destination (OD) flow is essential for the development of intelligent transportation systems and effective urban traffic management. Existing approaches typically either predict passenger outflow of departure stations or inflow of destination stations. However, we argue that travelers generally have clearly defined departure and arrival stations, making these OD pairs inherently interconnected. Consequently, considering OD pairs as a unified entity more accurately reflects actual metro travel patterns and allows for analyzing potential spatio-temporal correlations between different OD pairs. To address these challenges, we propose a novel and effective urban metro OD flow prediction method (UMOD), comprising three core modules: a data embedding module, a temporal relation module, and a spatial relation module. The data embedding module projects raw OD pair inputs into hidden space representations, which are subsequently processed by the temporal and spatial relation modules to capture both inter-pair and intra-pair spatio-temporal dependencies. Experimental results on two real-world urban metro OD flow datasets demonstrate that adopting the OD pairs perspective is critical for accurate metro OD flow prediction. Our method outperforms existing approaches, delivering superior predictive performance.