Why humans (and all animal kingdom species) are bilaterally symmetric.

Why do humans (and all animal kingdom species) have a two-sided symmetry built into them (brains, nervous system, skeletal structure, etc.)?

The not so striking thing is that symmetry in ALL its forms and formats is a basic characteristic of nature, living and non-living.

From http://en.wikipedia.org/wiki/Symmetry:*
"The "precise" notions of symmetry have various measures and operational definitions. For example, symmetry may be observed:

• with respect to the passage of time;
• as a spatial relationship;
• through geometric transformations (scaling, reflection, rotation);
• through other kinds of functional transformations;
• as an aspect of abstract objects, theoretical models, language, music and even knowledge.^"

What IS striking though is that only in living forms WITH free mobility (the animal and insect kingdom and also the functionally movable parts - seeds and leaves - of the plant kingdom) that this symmetry is bi-lateral only:
They have a front and a back, as well as an up and a down side, but in one direction only: either horizontal (along the back and forth axis) or vertical (along the up and down axis) - but not perpendicular (along the from-left-to-right axis|), while in say the flora symmetry is multi-sided (except for a plant's mobile and motile parts such as seeds and leaves).

Why would that be?

• Just quickly for now and without any explanation: the one direction of sun rays (also  the sun moving clockwise in the northern hemisphere);
• the singular direction of attack approach by enemies (beasts of prey) or the escape route of potential victims (preyed upon beasts);
• for now also and only quickly focusing on the brain, could that be why one side of the brain has a more temporal / sequential and the other side a more spatial / linear character, or the one side is passive and the other side reactive?

Note:
* "In bilateral symmetry (also called plane symmetry), only one plane, called the sagittal plane, will divide an organism into roughly mirror image halves (with respect to external appearance only[ ]. Thus there is approximate reflection symmetry. Often the two halves can meaningfully be referred to as the right and left halves, e.g. in the case of an animal with a main direction of motion in the plane of symmetry. [ ]
Most animals are bilaterally symmetric, including humans [ ], and belong to the group Bilateria. [ ] Most bilateral animals have an identical shape on either side, as if bisected by a mirror. Bilateral symmetry permits streamlining, favors the formation of a central nerve center, contributes to cephalization, and promotes actively moving organisms. Bilateral symmetry is an aspect of both chordates and vertebrates.
[Only certain] flowers such as members of the orchid and pea families are bilaterally symmetrical [ ]. The leaves of most plants are also superficially bilaterally symmetrical"
(From http://en.wikipedia.org/wiki/Symmetry_%28biology%29#Bilateral_symmetry)