I hope my answer doesn't fall into the "no common answers" category, but I believe there are two very good reasons for avoiding antibiotic use.
One is that we tend to treat many bacterial issues with antibiotics despite questions about whether they are truly necessary. Ear infections are one area where antibiotics are commonly prescribed even though there is evidence that the majority of infections will heal in about the same amount of time without antibiotic treatment. When we overuse antibiotics we kill the bacteria that are susceptible to that antibiotic. The bacteria that are resistant can then multiply--and we already know they cannot be killed by that antibiotic. When scientists discuss development of resistant species of bacteria through overuse of antibiotics, this is what they refer to. We currently have strains of bacteria for which we have no reliable treatment--for example, Neisseria gonorrhoeae, which causes gonorrhea.
Another issue is that our bodies naturally have many, many helpful bacteria. The bacteria in our digestive tracts help us digest our food. When we use antibiotics we can disrupt the natural population of bacteria living in our bodies.