Underground fluid-injection operations, such as hydraulic fracturing and enhanced geothermal stimulation, have triggered multiple earthquakes across the globe. Earthquake nucleation models within the rate-and-state friction framework suggest that an increase in fluid pressure favors stable slip. However, certain observations indicate that fluid injected into faults may reduce effective normal stress, promoting fault failure, which highlights the debate on the role of fluids in controlling earthquake fault stability. This paper proposes a rate-and-state friction-based model of earthquake nucleation that incorporates fluid injection and diffusion processes, and extends the stability criteria of the system. The results show that fluid pressure heterogeneity can indeed influence fault stability. Elevated fluid pressure stabilizes faults, however, fluid pressure heterogeneity counteracts this stabilizing effect. The model suggests that pressure heterogeneity above a certain threshold facilitates seismic slip, whereas heterogeneity below this threshold can stabilize it. The results further indicate that this threshold reflects a universal instability criterion inherent to the system, rather than an incidental product of a specific fault or rock type. Accordingly, this study proposes a pressure-heterogeneity index as an operational precursor: Tracking spatiotemporal pore-pressure heterogeneity can guide the traffic-light-style adaptive control of injection. These insights provide a new, mechanism-based explanation for the role of fluids in triggering earthquakes.