Why do planes need a small landing gear instead of a large gear?

It is all about minimizing size and weight and maximizing performance. They aim for the lightest and smallest components possible to do the required job. Extra weight and size of the landing gear means less cargo capacity, higher fuel consumption, and reduced performance. Keep in mind that lighter and smaller landing gear does not necessarily equate to being cheaper. Often times the engineering, metallurgy, and precision required for smaller landing gear has a much higher cost. However that usually has a quick payback in operating cost savings. The landing gear size relative to the aircraft size is usually due to the conditions of the desired airfield type. For example, commercial airliners are usually only operated from well maintained paved airfields so their tires and gear can be relatively small. Single engine bush planes often operate from creek beds and other rough terrain. Their tires are quite large relative to the rest of the aircraft.