Animals are mobile, they can simply move their bodies to where the resources are. Mobility benefits from symmetry, balance and motion are easier to ‘calculate’ if you have matching weights and lengths on either side. So symmetry has a natural advantage and becomes a sexual characteristic in many animals, including humans, which further reinforces the benefits of symmetry.
Plants are not mobile, if they sense nearby resources they have to grow in that direction. Ex a new branch will grow into an opening in the canopy to collect the light from above. It wouldn’t make any evolutionary sense to grow an opposing branch. So plants have no real benefit to symmetry. With one exception: where plants and animals interact, symmetry matters again (flowers).
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