  For a nitrogen dimer in insulating MgO, a ferromagnetic coupling between
spin-polarized $2p$-holes is revealed by calculations based on the density
functional theory amended by an on-site Coulomb interaction and corroborated by
the Hubbard model. It is shown that the ferromagnetic coupling is facilitated
by a T-shaped orbital arrangement of the $2p$-holes, which is in its turn
controlled by an intersite Coulomb interaction due to the directionality of the
$p$-orbitals. We thus conjecture that this interaction is an important
ingredient of ferromagnetism in band insulators with $2p$ dopants.
