One of the 20 rules of design, Rule #8 to be exact, states that sometimes when it comes to symmetry, the design of the image you make might become dull & flat. It also removes the flexibility of the elements that can’t work on a symmetrical design.
Let’s take these Walt Disney movie/TV Show posters for example:
Bad Example:
The way both the characters’ poses & the background are placed to give a symmetrical look feels generic & lazy, when you cut it in half, the left & right halves look too similar.
Good Example:
Now THIS is more like it! The log is tilted at an angle so there’s still balance, but NOT symmetry. Same with the river & the trees in the background. The left has more trees, while the river leans a little more to the right. Even the characters a placed in different positions because they all have different proportions that make them distinguishable, so they’re still balanced, while not having to rely on symmetry. The logo is the ONLY thing that is symmetrical, but even then it’s small enough to not matter.