The important role of unicellular flagellated micro-organisms in aquatic food webs is mediated by their flagella, which enable them to swim and generate feeding currents. The flagellum in many predatory flagellates is equipped with hairs (mastigonemes) that reverse the direction of thrust compared to the thrust due to a smooth flagellum. Conventionally, the mechanism of such reversal has been attributed to drag-based thrust of individual hairs, neglecting their hydrodynamic interactions. However, at natural densities of hairs, hydrodynamic interactions are important. In fact, using fully resolved three-dimensional computational fluid dynamics, we show here that hydrodynamic interactions are key to thrust-generation and reversal in hairy flagellates, making their hydrodynamics fundamentally different from the slender-body theory governing smooth flagella. We reveal the significant role of the curvature of the flagellum, and using model analysis we demonstrate that strongly curved flagellar waveforms are optimal for thrust-generation. Our results form a basis for understanding the diverse flagellar architectures and feeding modes of predatory flagellates.