As someone who has studied both math and computer science (and is now a professional programmer), I have no idea what you are talking about. We are far better at teaching people to program than we are at teaching them to do math. Its just that most people self select out of math [0], so, due to selection bias, it appears that we are great at teaching those that remain.

As an aside, as someone who also studied linguistics [1] (and a couple of foreign languages at a beginner level), I am very confident in saying that our approach to teaching natural languages relies almost entirely on natural aptitude. It is just that, absent a serious mental disorder, all humans have a very large natural aptitude for natural languages

[0] Probably because we are absolutly terrible at teaching it.

[1] I assume not what you mean by teaching natural languages, but the topic of language acuisition (including in adults) does come up; plus it gives some perspective on how teaching language would look if we didn't rely on natural aptitude.