By analogy with the selection rule governing the uniaxial magnetism of magnetic insulators, we found that the uniaxial magnetism of permanent magnets (i.e., itinerant or metallic ferromagnets) requires the presence of a strong polarization (i.e., unequal populations of the two members constituting a pair) in one of the three rotationally degenerate pairs, (<i>xz</i>², <i>yz</i>²), [<i>xyz</i>, (<i>x</i>² - <i>y</i>²)<i>z</i>], and [<i>x</i>(<i>x</i>² - 3<i>y</i>²), <i>y</i>(<i>y</i>² - 3<i>x</i>²)], of the f-bands in rare-earth (RE)-based ones, and in one of the two rotationally degenerate pairs, (<i>xz</i>, <i>yz</i>) and (<i>xy</i>, <i>x</i>² - <i>y</i>²), of the d-bands in RE-free ones. This requirement was confirmed by determining the magnetocrystalline anisotropy energies (MAEs) of permanent magnets SmCo₅ and MnAl as well as the partial density of states (PDOS) plots of their rotationally degenerate pairs of bands on the basis of density functional theory (DFT) calculations. As a quantitative measure for the strength of the pair-polarization in each rotationally degenerate pair of bands, we defined the pair-polarization index Δ<i>p</i>, which is associated with the calculated PDOS plots. Finally, we presented qualitative arguments with which to explain why a strong pair-polarization occurs in a particular rotationally degenerate pair in both RE-based and RE-free permanent magnets.