If stress is quickly ramped up, the rock can't keep pace and will fracture. If stress is slowly increased or held constant, the rock can keep up and will deform in ductile fashion. Because the deformation accrues slowly, we say that the strain rate is slow. Strain rates in nature are incredibly slow. That's a long time, but Nature has nothing but time.
Some minerals are more ductile than others.
For instance, calcite and micas are quite ductile, whereas pyroxenes and olivines are not. Rocks with lots of mica will be more likely to respond in a ductile fashion that will rocks rich in olivine. Water, either in the crystalline structure or between grains, makes rocks much more ductile. Rocks in the continental crust are quartz-rich and wet. On the whole, they behave like wet quartz.