The rule of thirds is about how a picture is composed in the viewfinder or in cropping it afterwards. In using the rule, the point is to make the picture more interesting to the viewer. Perfectly balanced placement (rule of halves{I just made it.}) where picture elements make divisions of the view into halves look static, whereas unbalanced divisions, as in thirds, is dynamic to the viewing eye. Dynamic views create a sense of movement in the picture in the viewer. The feeling induced is that something is going on. Where otherwise the feeling is a boring fixedness.

Actually making this fact of visual psychology a rule as with many other made rules can be straight jacket inhibiting an occasional creative opportunity. The fact should be rather regarded as guide that applies in many compositions, but volition of which is not necessarily bad in appropriate situations.

What is an appropriate situation? The ability to identify that is the difference between a picture taker and a photographer, and one of the reasons to hang around this site trying to hone the visual sense to recognize them. Otherwise, the rule of thirds is helpful more often than not.

Don't go taking a scale of measure to your photography. Develop your eye's sense of proportion. In your efforts to make better pictures through examples, go beyond simplistic viewing. It is not enough think, "gorgeous, pretty, beautiful, great, tremendous", and all those other expressions of admiration. Pick out what it is in the example honing awareness of visual details. Get analytical. Getting there is a process requiring time, effort, patience, and devotion to the objective.