Doctors used to prescribe antibiotics for a ton of stuff that wasn't affected by antibiotics(viruses), most are more careful these days. The issue most people have is that they aren't that good for you, are often used to try to treat things they can't treat, are overprescribed, the overuse of antibiotics leads to antibiotic resistant strains of bacteria - and if you can't treat it easily with antibiotics you can be kinda screwed.
I have friends who get these really bad infections that they can't get rid of without using very very strong antibiotics and they say it's because they were overtreated with antibiotics as a kid. Additionally if you are prescribed antibiotics you are supposed to take them as prescribed, not just stop taking them if you feel a little better (unless your doc says it's ok) because semi-treating something can help add to stronger bacterial strains (or something like that).
So that's the short form, as I understand it. Plus overuse of antibacterial soap adds to the super-strong bacteria world - it kills the weak ones, allowing the stronger ones to prosper.

Another concern though, antibiotic-wise, is meat - many of the animals raised for meat are treated prophylactically with antibiotics (to keep them healthy in feed lots etc where there are a huge number of animals and they can't risk a massive disease outbreak) and the antibiotics can end up in the meat that people eat, therefor raising the person's overall exposure to antibiotics. Plus antibiotics aren't meant to be taken all the time, just when you have a bacterial infection, so the meat thing is a real concern for many people - the solution being meat that hasn't been treated (which can be hard to find in some areas, a lot of the time you would have to look for pasture-raised and pasture-finished (or grass-finished) animals to eat, or not eat meat. Either way.

And others disagree completely and consider them to be safe in all cases, as long as they are taken as prescribed by a doctor.