Incomplete courses of antibiotics can allow weakly resistant bacteria to survive, multiple, and provide fertile ground for further mutations to produce string antibiotic resistance. The use of multiple antibiotics can lead to the same thing by allowing more bacteria to be exposed to more antibiotics to select for resistant strains.
Work Step by Step
Basically, antibiotics function as selective agents for resistance to themselves. Overuse in either of the ways described in the question lead more quickly to the development of resistance in many environmental samples of bacteria, defeating the usefulness of those same antibiotics.