[BobaFloutist]

>the way German-speaking people think about their grammar is often different from how foreigners think about the German grammar. The rules end up with the same result, but the angle can often be different.

That's true for most languages, native speakers are almost universally terrible at explaining rules because they just intrinsically know them and never have to name or even think of the rule. To the extent that native speakers are formally taught grammar, it's usually edge cases, formal registers, and more sophisticated tools, none of which are the primary concern of language learners.

[int_19h]

It really depends on the country. E.g. in Russia the formal grammar is taught in school very thoroughly, with the complete declension table etc.