Finite difference-based micromagnetic simulations are a powerful tool for the computational investigation of magnetic structures. In this article, we demonstrate how the discretization of continuous micromagnetic equations introduces a numerical “discretization anisotropy.” We demonstrate that, in certain scenarios, this anisotropy operates on an energy scale comparable to that of intrinsic physical phenomena. Furthermore, we illustrate that selecting appropriate finite difference stencils and minimizing the size of the discretization cells are effective strategies to mitigate the discretization anisotropy.