copypasta for science
"The adults of all extant echinoderms are radially symmetrical. A superficial bilateral organization has evolved twice, in irregular echinoids and holothuroids, but is based on an underlying five-fold organization of skeleton and most organ systems, and is clearly secondary. Higher order radial symmetry (e.g., seven-fold or nine-fold) has evolved on several occasions, and is also clearly a secondary modification. The evolutionary origins of five-fold symmetry remain obscure. Some early Paleozoic echinoderms are not radially symmetrical (e.g., carpoids and helicoplacoids), while a possible echinoderm from the Vendian (Arkarua) has five-fold radial body organization."
But seriously, bilateral and radial symmetry are part of our evolutionary lineage. It was one of the first traits to develop in multicellular organisms, and that trait is common to all that original species descendants.
Look up phylogenetic trees, each node is defined by a trait, where a novel feature causes a branch in the tree. Bilateral symmetry is one of the very first branches after prokaryotes became eukaryotes and became multicellular.
It stems from the various chemical signals used to move cells into proper place during growth/development. You can't really do one side and not the other if you grow out from the middle and use chemical signals to places cells in the proper places.
Phylogenetic tree information:
http://tolweb.org/tree/Click a node, it tells you what characteristics define that group.