bilateria as :
animals with bilateral symmetry, i.e., they have a head ("anterior") and a tail ("posterior") as well as a back ("dorsal") and a belly ("ventral"); therefore they also have a left side and a right side.
By symmetry, I understand that divisions of the body along some plane be similar. Now, if you have a head and tail, isn't the horizontal symmetry lost (head and tail look different) ? Similarly, for a vertical division, a different looking belly and back also destroys symmetry along this axis.
An organism whose head and tail are exactly the same (you can't even make out if something is head, and the other, tail), is perhaps "actually" bilaterally symmetrical (along the horizontal axis).
What am I missing here ?