QUOTE(wiki)
A longitudinal fissure separates the human brain into two, distinct cerebral hemispheres connected by the corpus callosum. The sides resemble each other, and, generally, each hemisphere's structure is mirrored by the other side, yet, despite the strong similarities, the functions of each cortical hemisphere are different.
Popular psychology tends to make broad and sometimes pseudoscientific generalizations about certain functions (e.g. logic, creativity) being lateral, that is, located in either the right or the left side of the brain. Researchers often criticise popular psychology for this, because the popular lateralizations often are distributed across both hemispheres, [1] however, mental processing is divided between them.
This does not mean there is no left or right side of the brain. It just means it has been dumbed down for popular culture - just like your post states. However your post also states there is no left or right side of the brain, which is wrong on several levels.