Larger Specimens
Some specimens a microscopist might be interested in viewing qualify as microscopic but are still relatively large. An example would be viewing the overall form of a plant cell. There are structures within the cell that may reveal themselves in greater detail when viewed with a higher-powered objective, but the overall view may be better under low power. This is a matter of preference for the microscopist.
Moving Objects
Instruments like binoculars, telescopes and microscopes feature what's termed a "field of view." This means that the viewer has a sort of tunnel vision when using the instrument. Unlike naked-eye vision, when peering through the microscope, there is limited peripheral view and turning the head and looking in another direction to follow an object is not an option. Because the field of view becomes smaller with higher-powered objectives, specimens that are moving can be difficult to observe under high power. They can quickly move outside the microscopist's viewable area. So the low-power objective is better suited to this situation.
Clarity
With high-quality microscopes, clarity is not much of an issue, but with mid-to-low-quality instruments, inferior optics can create a view with poor resolution. This problem is exacerbated when viewing through higher-powered objectives. The solution is to compromise by using a lower-power objective, sacrificing some magnification for a better-quality image.
Centering
Often the microscopist will want to view a specimen under high power. Simply beginning with a high-power objective, however, is often not the best approach. Finding a specimen in the field of view and getting it into focus can be very difficult when beginning with a high-powered objective. The solution to this problem is to begin with a low-power objective. This aids greatly in finding the object and bringing it into focus. Once this is accomplished, the microscopist can then switch to a higher-powered objective.