We present the science drivers for the far-infrared enhanced survey spectrometer (FIRESS), one of two science instruments on the PRobe Infrared Mission for Astrophysics. FIRESS is designed to meet science objectives in the areas of the origins of planetary atmospheres, the co-evolution of galaxies and supermassive black holes, and the buildup of heavy elements in the universe. In addition to these drivers, FIRESS is envisioned as a versatile far-infrared spectrometer, capable of addressing science questions in most areas of astrophysics and planetary astronomy as part of a dominant General Observer (GO) program with 2/3 of the current science cases using FIRESS. We summarize how the instrument design choices and parameters enable the main science drivers as well as a broad and vibrant GO program.