Because this is a better representation than what I drew on the board.
“The theory is that if you place points of interest in the intersections or along the lines that your photo becomes more balanced and will enable a viewer of the image to interact with it more naturally. Studies have shown that when viewing images that people’s eyes usually go to one of the intersection points most naturally rather than the center of the shot – using the rule of thirds works with this natural way of viewing an image rather than working against it. ” — From an article by the Digital Photography School. Full article and pictures of more examples on the rule is here.