Swearing relies on sophisticated structures in both right and left hemispheres but it also draws on one of the most primitive parts of the early brain. What does this mean in practice? Well, if swearing were a simple, primal thing we wouldn’t expect to see so much involvement from the more recent, more complicated areas of the brain. However, if swearing weren’t so closely linked to our emotions, the amygdala wouldn’t have such an important role to play. And the fact that swearing is lost if we lose our ability to map the emotions of others shows us just how socially sophisticated we have to be in order to swear.
Which answers the old accusation that swearing is a base response. It's actually quite sophisticated.
What the quote does not show is the background that Byrne gives about the anatomy of the brain, its functions, and its development. There is more to the book than simple statements like the above just thrown around.
There is also a great description of various experiments that tried to measure the effectiveness of swearing as pain relief.
I rather like the book so far.