I think it's because empathy is something a bunch of humans want to have and display and fairy types generally do that more than other pokemon
This is definitely a part of it, but I also think that a lot of it is selection bias. You gotta consider the overlap of people who are really into Pokemon, and also choose to take in-depth personality quizzes - lotta Fairy-type energy in there!
Someday, when this test is common in higher academia, maybe I'll have a more accurate sense of these things...