I think the mechanism might work like this (disclaimer, I'm not a doctor, I'm just making a theoretical guess): What can an antibiotic do? Kill bacteria that a

I think the mechanism might work like this (disclaimer, I'm not a doctor, I'm just making a theoretical guess): What can an antibiotic do? Kill bacteria that are not resistant to it. If a bacterium is resistant to it, it will be unaffected. Now, if you stop taking it "early" the antibiotic didn't have the time to kill 100% of non-resistant bacteria. You leave your body in a mixed environment where non-resistant and resistant bacteria have to compete. If you keep taking it once you feel better maybe you killed all the non-resistant bacteria. So you leave your body in an homogeneous environment where only resistant bacteria live, don't have to compete, and can prosper undisturbed.