The Clefairy seem powerfully drawn to nighttime and moonlight, seeming to prefer it to the daytime. In many different mythologies, the moon has been associated with femininity (especially menstrual cycles), and a changeable nature, as well as the rise of supernatural activity/strange occurrences (thus the word "lunatic" deriving from "luna," meaning moon).
The moon in mythological stories is often seen as equal to or a little bit lesser than the sun, but it "rules" over a vastly different time of day, when humans are generally asleep and nocturnal (or fantastical) activity can take place. This is why many cultures and religions have sought to draw power from the moon, or viewed each phase of the moon as spiritually or magically significant. For instance, in China, some make ritual offerings on the night of the full moon, and in the Wiccan religion, important rituals are often held at various points during the moon's major phases. Also, the gender of most moon deities in world religions is female, but there are a few male ones as well--this syncs up with the percentage of bred Clefairy being 75% female and 25% male!
In addition to the lunar religious and gender connections, music, dance, and the arts in general have also been associated with the moon, since artistic inspiration seems as changeable as the moon's face. Lastly, there are some who believe that the Moon is actually a hollow spacecraft with aliens living in it--which may be where the idea of the Clefairy's origins came from in the Pokemon universe!
As a night owl myself, I've grown up appreciating moonlight and nighttime as well--it's an easier time of day for me to be awake, because it's not so hot and bright, and I've finally gotten my nap out. (I may not be as shy as a Clefairy, but you won't see me hopping around at 6am unless I'm hyper and haven't gone to bed yet!) I've also loved its simple, slowly changing beauty in the night sky, adding its gentle, silvery light to even the darkest landscapes.