Sea ice motion is driven by winds and ocean currents. This motion is accommodated through deformation that localizes along well-defined fracture lines, where sea ice can slide (shear), move apart (divergence), or ridge (convergence). Most large-scale models treat sea ice as a continuum and use the Viscous-Plastic (VP) rheology to describe its mechanical behavior, primarily for its computational efficiency. The VP rheology combines two regimes: at very small strain rates, sea ice behaves as a highly viscous material, mimicking the elastic deformations observed in sea ice, while beyond a yield threshold, it undergoes irreversible plastic deformation. However, a linear stability analysis shows that the plastic regime of the VP rheology is ill-posed, indicating that the perturbation growth rate increases without bound. Using idealized numerical experiments, we show that solutions obtained with the VP rheology are resolution-dependent, consistent with the problem's ill-posedness. We further demonstrate that the viscous regime drives the initial amplification of the instabilities through energy growth linked to a transfer from potential to kinetic energy, akin to shallow-water waves. Preliminary results suggest that a new ice strength parametrization makes the VP rheology well-posed. As sea ice models move toward higher spatial resolutions, these findings underscore the importance of critically assessing the physical relevance of the rheologies currently in use.