In some languages, "learn" and "teach" are the same word.
For example in Czech, the former is in reflexive form, to "teach oneself".
učit se (learn) and učit (teach)
And in other languages, the meaning of "teach" can be expressed using the word for "learn", by adding the learner as indirect/transitive object:
to learn someone how to play the piano
But I don't know what the parent comment meant by this:
> the learn/teach distinction was made up by grammarians
That distinction exists in some languages, and not in others. Perhaps they mean that this difference didn't used to exist in English, but in later years grammarians popularized it..?
Looking up the etymology of "learn", I found the answer.
> Transitive use (He learned me (how) to read), now considered vulgar (except in reflexive expressions, I learn English), was acceptable from c. 1200 until early 19c.