Abstract: Based on the Brueckner-Hartree-Fock approach combined with the Hellmann-Feynman theorem, this work systematically investigates the contributions of different operator terms, components of nuclear force, and kinetic terms to the nuclear matter symmetry energy within the density range of 0.1 \sim 0.5 fm⁻³, employing the local Idaho chiral interaction at at various chiral orders and regulator values. For comparison, results obtained adopting the Av18 potential are also presented. Compared to the Av18 potential, the Idaho chiral interaction predicts a stiffer density dependence of the symmetry energy, with the kinetic term playing a more significant role in the symmetry energy. Additionally, the tensor force V_\textt and central force V_\textc jointly dominate the evolution of the symmetry energy under the Idaho chiral interaction. The contribution of the central force to the sumetry energy enhances with increasing chiral order and the softing the regulator, while the tensor force contribution to symmetry energy exhibits the opposite behavior. Notably, at N³LO with a regulator (R_\textπ,R_\mathrmct) = (1.2,0.75) fm, the contribution from the central force surpasses that of the tensor force.In contrast, under the Av18 interaction, although the V_(\boldsymbolL\cdot\boldsymbolS)^2 term makes a significant contribution to the symmetry energy at high densities, the tensor force remains the dominant role in the symmetry energy. These findings indicate that the tensor force plays a crucial role in determining the symmetry energy under both the Idaho chiral and Av18 interactions. However, its specific contribution exhibits strong model dependence. This study not only further highlights the importance of the tensor force in nuclear physics but also identifies the key components governing the symmetry energy under the Idaho chiral interaction, thus providing new insight into its microscopic origin.