Grammar Rules and Explanations

Sorry it has been so long since my last posting, but I'm back! I came across this quotation in Thornbury's chapter "How to Teach Grammar from Rules," and I wanted to share it with you.

He says, "The point was made that it is not often the case that a linguist's version of a rule will be appropriate in a classroom context, and there will inevitably be, therefore, some trade-off between the truthfulness of a rule and the pedagogical worth of a rule" (p. 32).

I find the last part particularly interesting and I wanted to get your opinion on it. What do you think he means by "truthfulness" and "pedagogical worth"? How can being aware of the difference make us better grammar teachers?