How does drug resistance develop in bacteria?
When antibiotics are prescribed to fight off a bacterial infection, there are already bacteria present in the common population that are resistant to that antibiotic.
As treatment ensues, the bacteria that are not resistant to the antibiotic die off fairly quickly; however, the mutants that are resistant take a lot longer to die off.
Thus, if a patient were to stop taking their antibiotics sooner than they were told to because they felt better, this would allow the resistant bacteria to rebound in far larger numbers than before (since there are no more non-resistant bacteria left).
If this happens, the patient now has an infection that is resistant to the antibiotic they were taking before, which requires a far stronger antibiotic to treat.
Hope this helps!