An itinerant ferromagnet with a cubic structure such as α-Fe has no uniaxial magnetism, while uranium monosulfide US has the strongest-known uniaxial magnetism despite its cubic structure. We probed the cause for this difference by density functional theory (DFT) calculations for α-Fe, FeNi, and US to determine their magnetocrystalline anisotropy energies (MAEs), partial density of states (PDOS) plots, and pair polarization indexes (i.e., the strengths of the pair polarizations), Δ<i>p</i>. By comparing these results with those already reported for MnAl and SmCo₅, we find that the MAEs of these itinerant ferromagnets increase in the order, α-Fe < FeNi < MnAl < SmCo₅ < US, and so do their Δ<i>p</i> values, revealing that US and α-Fe differ in their uniaxial magnetism due to the large difference in their pair polarizations. We also investigated the possibility for pair polarization to induce Jahn-Teller instability by analyzing the weak cubic-to-rhombohedral distortion of US that accompanies its ferromagnetic transition at 177 K to show that this is indeed a weak Jahn-Teller distortion. The absence of such a Jahn-Teller instability in other permanent magnets was ascribed to the weak covalent character of their interatomic bonds.