Do you have any scientific evidence to back up your theory? Or, said another way, where is this science you speak of documented and tested?
As far as evidence against your theory, evolution (e.g. bacteria becoming resistant to antibiotics) is the result of mutation and selective pressure. If antibiotics are never used, then there is no selective pressure. Significant percentages of a bacterial species do not just decide to become immune to some antibiotic that doesn't exist or is never used.
When the selective pressure of an antibiotic is present, however, those mutations that provide immunity to the antibiotic are selected (as the others die) and become a larger percentage of the total population of the species.
This is also why you take the full dosage of an antibiotic. Otherwise, you leave the most resistant alive (those more vulnerable to the antibiotic die first, in theory).
Also why farms are considered to be the leading cause of antibiotic resistance. By constantly administering antibiotics when they are not needed, you are providing a constant selective pressure, forcing adaptation to occur.
Bleach is vastly more effective at sterilization than any known antibiotic. Their only advantage is inside an organism by nocking things back immune systems can win. However, for example in imunocompromized people they have minimal effect.
It's well known that bacteria live and reproduce outside the human body. Many strains, like listeria or salmonella, can live in food, outside of any human or animal host. Cholera lives in sewage. Also, animals are reservoirs for a large number of bacterial species. Unless we're going to dose all humans, all animals, and the environment as well, then we're not going to succeed.
Further, 80% or so of most antibiotics get excreted right out of the body in urine within a matter of hours. This means that the environment is going to get dosed with a low level of antibiotics, just the perfect environment for breeding immunity.
Finally, bacteria can exchange plasmids inter-species, so if some innocuous bacterium in the environment develops immunity, it can transfer that to a virulent species at a later time.
I think however it's not enough to conclude that consciously avoiding using antibiotics provides a net gain.
It, in my mind, becomes a bit of an economics question if you consider the trade-offs. Not dosing cattle could to food poisoning which could lead to higher human consumption of antibiotics.
I also have a fear of this becoming a panic, much like the anti-vaccine panic which leads people away from getting proper medical treatment.
It is a famous and time-honored rationalization that sidesteps doing the right thing because the wrong thing is certain to occur anyway. The logic is faulty and self-serving, of course. Sometimes someone else won't do it. The soldiers asked to fire on their own people when the Iron Curtain governments were crumbling all refused, one after another. Sometimes someone else does it, but the impact of the refusal leads to a good result anyway. When Elliot Richardson was ordered by Richard Nixon to fire Watergate Special Prosecutor Archibald Cox, he refused and resigned. Cox ended up being fired anyway, but Richardson's protest helped turn public opinion against the White House. Even if neither of these are the final result, the individual's determination to do right is always desirable in itself. The Futility Illusion is just a sad alternative to courage.