Differential gears don't turn, or turn very little, in relation to each other in normal driving. The load is applied at 90 degrees, and not through turning gearsets.
Only when taking a turn is there a difference between left and right, and one will rotate around the other a little.
When wheelspinning, one side is stationary, and the other is rotating madly around. This wipes out oil quickly on the bearing cups, and the gears don't take well to this kind of movement - they will pit, chip, and gall.