AP shells do a lot of damage if they penetrate (but not over-penetrate), but if they don't, then it's better to use high-explosive shells because they reliably do mediocre damage and can set the enemy on fire.
So, in case of destroyers, if you use AP shells:
- against battleships or heavy cruisers, your shells will just bounce off their armor, causing zero damage.
- against destroyers or light cruisers, your shells will over-penetrate, doing less damage than HE shells.
Maybe there are a few light cruisers where AP shells could be effective, I didn't yet find any.
So, are there situations when it makes sense to fire AP shells from destroyers?