If your doctor actually doesn't know why it's necessary to take the full course of antibiotics (antibiotic resistance), please get a new doctor. Seriously. (And report the old one, since he/she should not be practicing).
Of course, if the problem is simply that you can't get a layperson-intelligible answer from them, or get enough time with them for them to explain it to you, or if they're willing to explain it to you, but only if you ask... that's another story, and much more commonplace.
The sad truth is, even for the most compassionate, attentive, dedicated doctor - the one who would always go the extra mile to provide you with the best care imaginable - over the years, it's become increasingly difficult (read: next-to-impossible) to dedicate that extra time to the patient unless they really press for it. Insurance reimbursements have been cut to the point where the only way most physicians can stay afloat is to make their practice a volume game[0]. As the patient, you're not actually the paying customer (the insurer is), and the insurer doesn't care if the doctor takes an extra five minutes to talk about bacterial resistance and evolution. They'll reimburse him/her the same amount either way[1].
The exception to this is high-end, self-paying practices (think 'concierge medicine'). Unsurprisingly, those tend to have the best service (of course, you pay heavily for this).
[0] Or to go bankrupt, and sell to a hospital/practice group. Which is subject to the same pressure to generate volume, except the hospital cares a lot less about you, the patient, on an emotional level than a private practitioner does.
[1] In fact, in the worst case, the provider is getting reimbursed exactly $0 for providing you this care, because you're on a capitated plan. Under captitation, the provider (usually a hospital) gets a fixed, annual amount per patient that they are responsible for, and that's all the payment they ever get. The idea there is that it discourages unnecessary care - which is true, but it also disincentivizes necessary care as well. And spending an extra 5 minutes to educate the patient in a way that may have an impact on broader public health, but is unlikely to affect their own actual care in any measurable way? They don't have time for that, and they're certainly not getting paid for it.