Antibiotics are selective agents, killing any bacteria which lack a gene to code for resistance to the antibiotic. Overuse of antibiotics leads to rapid selection of resistance to the antibiotic and, thus, makes the antibiotics useless when trying to eliminate infection.
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Overusing antibiotics allows selection, in this case artificial selection since humans are, inadvertently, selecting for resistant bacteria. This leads to a large stock of resistant bacteria in the environment, so that any infection which they create is likely not to be eliminated by the antibiotics which were overused. Thus, overuse of antibiotics creates a health hazard by selecting for resistant individuals in the population of bacteria which were meant to be killed in the first place.