You might want to compare iron(II) not with neutral iron, but with neutral chromium.
Both iron(II) and neutral chromium have 24 electrons, but there the similarity ends:
$\ce{Fe^{2+}}: [\text{Ar}]3d^6$
$\ce{Cr^{0}}: [\text{Ar}]3d^54s^1$
Think of the Bohr model. According to this model the energy level of electrons depends only on the shell number $n$, so we would expect 24 electrons to follow the $[\text{Ar}]3d^6$ configuration. In real life that happens exactly only for single-electron atoms where there are only electron-nucleus interactions. When there are electron-electron interactions they could fill the shells not in order, like the chromium atom described above.
But in a multielectron atom, if you add more nuclear charge you make the electron-nucleus interaction stronger, and the Bohr-model configuration becomes more favorable. One might suppose that dozens of added protons might be needed to get chromium's $[\text{Ar}]3d^54s^1$ to the Bohr-predicted $[\text{Ar}]3d^6$. Instead, the energies of the two configurations are so closely spaced that two extra protons, converting neutral chromium to ferrous iron, is enough.