Why is it best to use the right size of drill bit in boring holes?

It all depends on what you are constructing. If the hole is required for some kind of fastener, if it is too small the fastener will not slide through. If to slack, the unit may fail when put into use, by allowing movement and wear, causing early fatigue.
During specialist construction (say for aircraft) some holes are drilled slightly under size and then reamed out, for a perfect fit.
For wood screws, the pilot hole must allow enough material for the thread to grip, but without pinching the screw, making it difficult to tighten up.