Scientists and physicians are concerned about the overuse of antibiotics because the more they are utilized, the greater the risk that a particular microbe will develop immunity to the drug, potentially morphing into the dreaded "superbug" everyone fears; one that is immune to our normal arsenal of pathogen fighting materials and capable of causing a dearly pandemic.
Bacteria are evolution's poster-child for adaptability. They can reproduce in as little as a few minutes to a few hours, depending on the strain. So it doesn't take long for them to reproduce generation after generation. Just like people, with each new generation comes genetic diversity and slight alterations to the DNA code. Bacteria are also single-celled organisms that can quickly adapt to their environment, passing on desirable traits onto their offspring. When life forms of any kind are exposed to a particular environment over generations, they tend to adapt accordingly. Thus the more you expose a virus to a threat (antibiotics), the more it will respond to that threat and the greater the odds that a random mutation will trigger immunity. Natural selection then kicks in, meaning the ones that survive to reproduce are those that are immune to the antibiotics, and so before long, the entire strain morphs into a resistant one; consisting almost exclusively of those that have survived through their genetic immunity. It's possible for a strain to go from as little as 1-2% immunity to a particular drug to as much as 99% in a single year.
This is also why it's important to use up all prescribed antibiotics, even if you feel better. Not eliminating the bug completely while subjecting those microorganisms that are in your body to antibiotics could cause it to come back with immunity to the drug you're taking, and then you're in far worse shape. Doctors even tier antibiotics for this reason; there are stage 1 drugs, stage 2, stage 3, etc., each slightly different and more powerful than the rest. In some cases, a particular strain of virus will develop immunity to all antibiotics available, and then doctors are helpless to do anything.
One more side note: this is why immunizations are much better than trying to treat an illness with drugs later. Immunizations build the immune systems own antibodies, so it develops a means for attacking the virus itself. A virus can't develop immunity to the natural immune system in the same way it can outpace antibiotics.
*Notice: Answers published here are general guidelines only, and are not a substitute for firsthand medical advice from a physician.