I agree but I felt like giving a slightly different explanation. It is not guaranteed that you are exposed to only one variant of a pathogen as they are constantly undergoing mutation. By increasing the exposure to an antimicrobial agent, selective pressure is applied against susceptible organism variants which will increase the overall proportion of a global population that are resistant to that agent. The mitigation for this is to take enough of the antibiotic to destroy these variants as well, although this is a somewhat "leaky" containment task as you may spread the pathogen to others while undergoing treatment. This analysis so far neglects that there are other microbes in your system that you are also exposing to the antibiotic even nonpathogenic organisms that we don't normally consider when discussing antibiotic resistance. However, due to horizontal gene transfer, even nonpathogenic organisms can potentially share any developed resistances with pathogenic organisms at a later time. The only real way to protect antimicrobial agents from resistance growth is to use them extremely sparingly. Multi-drug resistant organisms have gotten bad enough that they have brought back the use of Colistin, a very old and fairly toxic drug that had fallen out of use for decades to use in cases where no other drugs work. If the world continues using these drugs at the current rate, we may see things like this become far more common.
Fundamentally we are in a war, pitting our multicellular intellect and biotechnology against our single celled brethren. It isn't as lopsided of a battle as it should be. What bacteria etc lack in individual strength, they more than make up for in multitude. I am fairly confident that in the long run we will out-innovate them but the needed systemic incentives are not currently in place to sustain our technological advantage at the present rate of resistance development.