Ionic solids are brittle due to the organization of their lattice structures. When layers of the lattice structure shift, ionic repulsion causes the lattice to break down into smaller pieces.
According to Aus-e-Tute, the lattice structure of ionic solids is arranged such that cations are surrounded by anions. The lattice arrangement causes many ionic solids to have crystalline structures. When the lattice structure shifts due to a stressor, it causes ions of identical charge to be brought closer together. Since ions of the same charge repel each other, the lattice structure breaks down. According to IB Chemistry, breaking crystalline structures causes a break along cleavage planes.