How does not completing a course of antibiotics lead to increased immunity within a population of bacteria?

As you take the antibiotics, it begins to kill bacteria causing infection within your body, however not all bacteria are created equal, and some are more resilient to the antibiotics than others. Naturally, the weakest bacteria die off first, so as you keep taking the drug, you are only left with the hardiest, most resilient ones that take the most antibiotics to kill, its normally about this time that you'll start to feel better.

However, if you suddenly stop taking the antibiotics, these bacteria will still remain, and then start to multiply again. What this will result in is an entirely new population of bacteria that all have this resistant trait, and so will now require even more antibiotics in order to clear the infection

(I would include a diagram with dots representing bacteria, with darker ones being the more resistant ones, to visually demonstrate what it might look like as the proportions change)