It is generally stated that it is important to finish a course of antibiotics because if you don't you can create antibiotic-resistant bacteria.
The logic normally given is that bacteria reproduce very quickly and mutate/evolve which each division and that one of these divisions could yield a resistant phenotype. However my primitive logic here is: if the bacteria has evolved resistance, what would it matter if you continued taking the antibiotics or not as you can no longer kill it now by taking the rest of your remaining course of antibiotics.
Perhaps it is a matter of semantics. I understand that bacteria could evolve to be more resilient to the antibiotic as the mechanisms of action of an antibiotic often involve multiple steps. In this case you should keep taking the course of the antibiotic to 'finish them off' before they get the chance to spread and go from resilient to resistant.