This has been linkjacked to oblivion. And I have not seen any compelling argument for right/left brainness based on viewing this image. It's merely an illusion that plays with your depth perception from lack of contrast and depth cues (motion parallax maybe, if you're so inclined).

I believe this is the original source of the image. http://www.procreo.jp/labo/labo13.html The author says nothing beyond it being a mysterious illusion.

The switching is as arbitrary as the coriolis effect. Try this thought experiment. Imagine instead of a woman, there was a perfect, black, sphere in the image. You couldn't tell if it was rotating at all. Now I add a protrusion to the "equator." Its length would vary in a sinusoidal fashion, and you could guess the ball is rotating, but still cannot reason it's direction. I can then successfully add protrusions such that it looks like a human and you wouldn't be able to tell; it's a simple lack of visual cues.

edit: my bad, not the coriolis effect. I was referring to the toilet-draining direction that is incorrectly attributed to the effect. The point is, given a little push in one direction, the water, or the image, would continue to rotate in that direction.