Good composition is often based upon the rule of thirds.  If you divide the scene into 9 rectangles of equal size (squares are equilateral rectangles), the points of interest should fall near the corners of the center rectangle.  Following this "rule" makes an eye pleasing composition, but it doesn't work well in all cases.  The truth is that the rule of thirds is not a rule, but a guideline.  It is useful for beginners to follow the rule, but not mandatory.  All too often, camera club judges place too much emphasis on the rule of thirds.  Art that is good may or may not follow rules.  The primary goal of art is to convey an emotional impact.  If it accomplishes that aim, the focal points won't be as important.  If you become good at using crayons to create art on blank paper, there is no need to color within the lines. 

Good artists know the "rules", but do not treat them as rules.  The "suggestion of thirds" just doesn't sound right, even if it is more correct in the actual usage by artists.  Notable exceptions to the rule of thirds include round or spherical shapes and spirals that fill the field of view.  If you have a subject that fills the frame and looks better to you when centered, do so.