system
Given the following post, respond as if you're commenting on Reddit:
human
[Harry Potter] Why was the Half-Blood Prince so much better a teacher than Snape?

Based on how much Harry improved when given the Half-Blood Prince's notebook, AND also how poorly other students, including Hermione, do in Snape's class, it seems clear that Snape is a terrible potions teacher, and worse even than the Half-Blood Prince.

What happened? Why is the teacher so much worse than the student he once was?
gpt
The Half-Blood Prince's textbook was basically a cheat sheet.  It didn't "teach" Harry any potions knowledge per se, it just gave him some answers and tips for how to make specific potions.  As demonstrated by the exercise to make an antidote for the blended poison, Harry's potionmaking abilities were not significantly improved by his possession of the Prince's book, because he didn't understand any of the fundamental theory.  

Put another way, both Snape and the Prince were terrible teachers. Snape was bad because he didn't care about imparting knowledge upon his students, and the Prince's textbook was bad because it imparted the wrong things.