The problem is that inappropriate use and overuse of antibiotics does do harm. There are many good reasons to not prescribe antibiotics unless they are clearly needed. Most uncomplicated virus infections get better within a few days. By prescribing antibiotics for these infections doctors increase parental demands for antibiotics. When the child gets better parents assume he is better because of the antibiotic since they haven't had an opportunity to see that children recover from these infections without medication.
All medicines have side effects.
When an antibiotic is used where it won't help, the patient risks experiencing these side effects without any potential benefit. Most of the side effects of antibiotics are just a nuisance, but some can be serious. When antibiotics are used without establishing a diagnosis there is a possibility that a more serious infection will be masked rather than cured. This can make it harder to come to the correct diagnosis and treatment down the road. Prescribing antibiotics at the first sign of illness before the diagnosis is established doesn't give children any opportunity to develop any immunity to infectious bacteria.