If a structure is not strong enough then an extra 1 or 2mm can make a difference.
But, if a material has poor fracture toughness, and fractures can travel at the speed of sound (for that material); then what difference does an extra 1 or 2mm make?
Fracture toughness can be more important than tensile strength to avoid structural / material failure.
CFRP Carbon Fibre Reinforced Plastic is poor in compression.
In a similar way that rope is good for pulling but poor for pushing.