Even when ionic compounds are strong (e.g. rubies and sapphires), they are neither malleable nor ductile in the slightest, and if sufficient stress is put on them, they will shatter, not bend. Why is that?
Ionic crystals are hard because of tight packing lattices, say, the positive and negative ions are strongly attached among themselves.
So, if mechanical pressure is applied to an ionic crystal then ions of similar charges may be forced to get closer to each other.
Now, by doing so, the electrostatic repulsion can be enough to split or disorient completely the lattice infrastructure. Thus imparting the brittle character.