Why half filled and completely filled orbitals have extra stability?
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Fully filled and half filled orbitals are exceptionally stable than any other configurations for an atom. In some cases like copper and chromium the electrons even leave the usual filling pattern for having an half or fully filled orbitals.
The famous quote of de Broglie goes like
Nature loves symmetry.
In half and fully filled configurations for an orbitals there more possibility for an electron to exchange its position with another degenerate electron. More possibility means more exchanges happening in that atom releasing more energy, particularly called exchange energy, hence accounting for that extra stability.
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