Symmetry is safe. It’s comfortable, non-threatening, and aesthetically pleasing. It can also be very dull. Using ‘asymmetrical balance’ can make things more interesting while still sticking to a grid to keep things ordered. In design, as in so many other things, the higher the risks the greater the potential rewards.
Symmetry has long been considered a good thing precisely because it is aesthetically pleasing and unchallenging to the eye. The word symmetry is derived from greek components which translate to ‘with measure’; symmetry is about proportion and balance, qualitative similarity as opposed to identical sameness. Asymmetry would therefore be a lack of balance or proportion, an unevenness.
In a visual context, however, most of us, even if we can’t remember taking basic geometry lessons (never mind what was in them) think of symmetry with a more restricted definition.