Actually, inhaling a bit of anti-bacterial cleaner probably won't kill that many bugs in your body at one time, if any, "good" or "bad".
When a doctor gives you an antibiotic, you are given a course which usually runs for a week or longer. You are directed to take the complete dose, even if you quickly feel better. The danger here is that if you stop treatment prematurely, you may not have killed all the targeted bacteria, and you may develope a strain of bacteria immune to the particular antibiotic. This is a serious health problem worldwide. Drug companies are always looking for new antibiotics, and some ab's are prescribed only if other common drugs fail to stop the infection.
So the real question isn't if we are making our immune system wusses, per se, but if we are making superbugs. Some folks think that that indiscriminate use of "antibacterial" cleaners and soaps is adding to this problem. So there is some validity to your question.
When I was a teaching assistant in a micro lab in college, we routinely used a dilute solution of bleach to clean our work areas before doing any culture work. Ethanol is also routinely used as a surface disinfectant in labs. Nothing fancy, but effective.