Many of my designs are, in some form, symmetrical. Part of this is just a personal preference, but in part, it is also simply human nature.
When viewing art, or experiencing anything for that matter, many people find they are more drawn to balance. Balanced colors, balanced lighting, balanced shapes - some sort or harmony that draws us in. For me, I find that making a balanced image, in many cases, leads me to something symmetric. making an asymmetric design more balanced is more difficult, for some people, but usually leads to a more interesting artwork.
I do challenge myself to make asymmetric design and still keep the balance that makes a work or art pleasing. That being said, I still often find that some great designs are completely symmetric.
This one, for example, is almost perfectly repeated around the center. Although there are subtle distinctions between the sides, the general shapes, colors, and lighting is fairly identical. I called it "Bluebirds" because the shapes at the center resembled the head of a bluebird.