I've thought about it, and I think now I'm able to better describe why I don't like Fluttershy.
In TV series or comics or whatevers, it can be entertaining when a seemingly harmless character has an unexpected moment of competence. For example, there was this one Batman story (I can't remember if it was a comic or an episode of TAS) where it turns out that, out of Batman's entire rogues gallery, Harley Quinn came closer to killing him than any of the others, including Mr. J himself. So this worked because it made the audience think, 'no way! ditzy and bubbly harley?'.
But with Fluttershy, they went way overboard. It seems that in every episode in which she has a prominent role, she overcomes pretty much all of her problems with ease after a small struggle of some kind. It wasn't too long before it became less 'whoa! she can do that?', and more 'ass pull in 3... 2...'.