Cross references:  Parazoa   Coelenterata    Protostome     Deuterostomes      Chordates     Hemichordates     Early Behavior       

Bilateria (Wiki) 
    "The bilateria are all animals having a bilateral symmetry, i.e. they have a front and a back end, as well as an upside and downside. Radially symmetrical animals like jellyfish have a topside and downside, but no front and back.  
    The bilateralia are a subregnum (a major group) of animals, including the majority of phyla; the most notable exceptions are the sponges, belonging to
Parazoa, and cnidarians belonging to Radiata.  
    For the most part, Bilateria have bodies that develop from three different germ layers, called the endoderm, mesoderm, and ectoderm. From this they are called triploblastic. Nearly all are bilaterally symmetrical, or approximately so. The most notable exception is the echinoderms, which achieve near-radial symmetry as adults, but are bilaterally symmetrical as larvae. "
The first evidence of bilateria in the fossil record comes from trace fossils in 
Ediacaran Period sediments, and the first bona fide bilaterian fossil is Kimberella, dating to 555 million years ago.[3] "   
There are two or more superphyla (main lineages) of Bilateria.
Deuterostomes  include the echinoderms,   HemichordatesChordates , and possibly a few smaller phyla.
Protostome include most of the rest, such as arthropods, annelids, mollusksFlat Worms , and so forth.  
    There are a number of differences, most notably in how the embryo develops. In particular, the first opening of the embryo becomes the mouth in 
  Protostome  , and the anus in  Deuterostomes  ."    
My comment
    If you're interested, you can learn a lot more by clicking on the links.       

Inversion (evolutionary biology) (Wiki)   
    "In evolutionary developmental biology, inversion refers to the hypothesis that during the course of animal evolution, the structures along the dorsoventral (DV) axis have taken on an orientation opposite that of the ancestral form.   
In the early 19th century, the French naturalist Étienne Geoffroy Saint-Hilaire noted that the organization of dorsal and ventral structures in arthropods is opposite that of
Mammals . Decades later, in light of Darwin’s theory of “descent with modification,” Anton Dohrn proposed that these groups arose from a common ancestor which possessed a body plan similar to that of modern annelids with a ventral nerve cord and dorsal heart.[1] Whereas this arrangement is retained in arthropods and other Protostome, in Chordates  Deuterostomes, the nerve cord is located dorsally and the heart ventrally. The inversion hypothesis was met with criticism each time it was proposed, and has periodically resurfaced and been rejected.[1] However, some modern molecular embryologists suggest that recent findings support the idea of inversion."   
In addition to the simple observation that the dorsoventral axes of protostomes and chordates appear to be inverted with respect to each other, molecular biology provides some support for the inversion hypothesis. The most notable piece of evidence comes from analysis of the genes involved in establishing the DV axis in these two groups.[2]  
    In the fruit fly Drosophila melanogaster, as well as in other protostomes, the β-type transforming growth factor (TGF-β) family member decapentaplegic (dpp) is expressed dorsally and is thought to suppress neural fate. On the ventral side of the embryo, a dpp inhibitor, short gastrulation (sog), is expressed, thus allowing nervous tissue to form ventrally. In chordates, the dpp homolog BMP-4 is expressed in the prospective ventral (non-neural) part of the embryo while several sog-like BMP inhibitors (Chordin, Noggin, Follistatin) are expressed dorsally.[1]
    Other patterning genes also show conserved domains of expression. The neural patterning genes vnd, ind, msh, and netrin are expressed in the Drosophila ventral nerve cells and midline mesectoderm. The chordate homologs of these genes, NK2, Gsh1/2, Msx1/3, and Netrin, are expressed in the dorsal neural tube. Furthermore, the tinman/Nkx2-5 gene is expressed very early in cells that will become the heart in both Drosophila (dorsally) and chordates (ventrally).[1]
My comment
  confirms my impression that the nerve cord in Protostomes  is ventral while in Deuterostomes  it's dorsal.         

Back in time: a new systematic proposal for the Bilateria (Goog)  
Full length HTML and PDF available online for free. 
Conventional wisdom suggests that bilateral organisms arose from ancestors that were radially, rather than bilaterally, symmetrical and, therefore, had a single body axis and no mesoderm.
We report phylogenetic analyses of bilaterian metazoans using quantitative (ribosomal, nuclear and expressed sequence tag sequences) and qualitative (HOX cluster genes and microRNA sets) markers. The phylogenetic trees obtained corroborate the position of acoel and nemertodermatid 
Flat Worms  as the earliest branching extant members of the Bilateria. "   
Because morphological and recent gene expression data suggest that
cnidarians , a phyla of the Coelenterata , are actually bilateral, the origin of the last common bilaterian ancestor has to be put back in time earlier than the cnidarians –bilaterian split in the form of a planuloid animal."      
My comments
The first  Bilateria  was the common ancestors of  cnidarians , a phyla of the Coelenterata , and  Flat Worms  .   Flat Worms  are already capable of quite complex behavior. 
2.  This article and the two references I looked at were not particularly helpful in understanding human psychology.  They did, however, provide some deep background.     
    Reference 1 
- 2004  
Origins of Bilateral Symmetry: Hox and Dpp Expression in a Sea Anemone 
Only abstract available online.     
    "Over 99% of modern animals are members of the evolutionary lineage Bilateria. The evolutionary success of Bilateria is credited partly to the origin of bilateral symmetry. Although animals of the phylum Cnidaria are not within the Bilateria, some representatives, such as the sea anemone Nematostella vectensis, exhibit bilateral symmetry.
    Reference 2 -
The radial-symmetric hydra and the evolution of the bilateral body plan: an old body became a young brain.
Only abstract available online. 
The radial symmetric cnidarians are regarded as being close to the common metazoan ancestor before bilaterality evolved. It is proposed that a large fraction of the body of this gastrula-like organism gave rise to the head of more evolved organisms. The trunk was added later in evolution from an unfolding of a narrow zone between the tentacles and the blastoporus. This implies that, counter intuitively, the foot of the hydra corresponds to the most anterior part (forebrain and heart) while the opening of the gastric column gave rise to the anus.
My comment
    This sounds more like
Deuterostomes than Protostomes .   

Early origin of the bilaterian developmental toolkit (Goog)  
Whole-genome sequences from the choanoflagellate Monosiga brevicollis, the placozoan Trichoplax adhaerens and the cnidarian Nematostella vectensis have confirmed results from comparative evolutionary developmental studies that much of the developmental toolkit once thought to be characteristic of bilaterians appeared much earlier in the evolution of animals."  

Acoela - Wikipedia   
The Acoela or acoels are a class of small and simple invertebrates in the phylum Xenacoelomorpha that resemble flatworms. Historically they were treated as an order of turbellarian flatworms, but molecular phylogeny studies revealed them to be basal bilaterians.[1][2]"