I actually feel like the left side of my body is male too!
There was a study by Dr. Ramachandran, a professor at University of California, San Diego, a few years ago that basically called this Alternating Gender Incongruity and basically suggested that whatever process happens to cause one to be transgender can sometimes only happen to one hemisphere of the brain. This study was largely not accepted, though I don't think it's underlying theory has really been dis-proven.
I tend to believe that's what happened with me. My left side is my guy side, my right side is my girl side, I am DMAB...I just live my life as Gender-Fluid, and why not?