That statement is true for normally consolidated CLAYS, which typically have an undrained strength which is lower than its drained strength.
After Duncan and Wight "Soil Strength and Slope Stability" - As is typical for normally consolidated clays, the undrained strength is lower than the drained strength. This is due to the fact that the pore pressure increases and the effective stress decreases during undrained shear. For very heavily overconsolidated clays, the reverse is true: The undrained strength is greater than the drained strength, because pore pressure decreases and effective stress increases during undrained shear.
Duncan and Wight are referring to the reason in differing behavior being due to the change in pore pressure. In simplistic terms, the soil grains in normally consolidated clay are spaced apart. When they are sheared (or loaded) they can re organise themselves into a tighter packing. As they are trying to "re organise" quickly, the water can not escape and pressure is applied to the water in the soil, which leads to an increase in pore pressure. The term "re organising" is typically called contracting, so normally consolidated CLAY are
contractive.
The opposite is true for heavily over consolidated CLAYs, as they have received a very large past pressure (pre consolidation stress) they have consolidated and the grains are tightly packed. When the are sheared (or loaded) they are already tightly packed and they need to "roll over each other" to try to arrange themselves in an even tighter packing. This "rolling over each other" means the soil grains are temporarily taking up more space (or volume). The "rolling over each other" is typically called dilating, so heavily over consolidated CLAYs are
dilative. See below image showing the grains rolling over each other.
The water is still there, however there is now more pore space to occupy, the water is drawn into the pore space which causes a negative pore pressure.