Why would a pilot want to land with less than full flaps?
Less flaps gives a faster approach speed. In some scenarios, a faster approach speed is better than a slow one, for example:


Strong crosswind
Possible wind shear
One-engine failure


A higher approach speed provides a better stall margin and higher control authority in challenging situations. For example, the Boeing 737 QRH calls for a flaps 15 landing in "One Engine Inoperative" and "Stabilizer Trim Inoperative" scenarios.

In the crosswind scenario, let's assume your approach speed is 100 knots, and the crosswind is 20 knots. The crosswind is therefore 1/5 of the approach speed, and you need a larger crab angle to keep the airplane aligned with the runway. If you increase your approach speed to 120 knots, then the crosswind is only 1/6 of the approach speed, and the crab angle is smaller, making landing easier.