Sometimes the Second Episode is the Problem that the Three Episode Rule protects against.

Some attempts to deconstruct the Three Episode rule focus mostly on defending the first episodes.

But a main reason I consider it important is how often I consider the exact second episode of a show to be one of it's worst.  Maybe some of you are thinking "well you don't need a Rule to not give up that quickly".  The thing is it's very easy for me to imagine finding a story's initial set up to be the only part of it that's good.   With American LA TV shows it's definitely happened a few times where I found a first episode pretty fun but as soon as they settled into their regular weekly routine I got bored of it.

Now when it comes to Anime where the second episode can give a potentially harmful early impression.  There are fortunately some that are episodic enough where I'm very willing to just recommend skipping the second episode entirely, at least on your first watch.

That is most heavily the case with A Certain Scientific Railgun.  What is so frustrating about the second episode isn't exactly something never in other episodes, but that's the only one where it's the main plot of the episode, and goes further with it then the show ever will again.  And it's not even filler in the Monster of the Week sense, but it fortunately has no actual connection to the Level Upper Arc.

The second episode of the 90s Sailor Moon Anime actually was skipped by the original DiC localization, so we have documented proof that it wasn't actually needed (thing is other episodes DiC skipped were among my favorites).  With Sailor Moon I'm kinda willing to tell people to just watch the 3rd episode first.

But in less episodic shows this goes back to the structural reasons the three episode rule exists.  The firs 3 episodes are often like an extended first act of a movie.  The first and 3rd episodes contain the most vital things that establish the world and initiate the plot.  The second episode can often be mostly necessary but less engaging connective tissue between them.

I also want to acknowledge the early Pokémon Anime here. In that case I really like the second episode but I know not everyone considers it great because of Suede's Pokémon Journey's review of it.  The second episode is to me filled with lots of fun stuff and it's certainly important set up and world building.  But it is indeed not as "tightly" written as episodes 1 and 3.