Feeling intuitive is when a person feels something to be true without conscious reasoning - it's basically using our instincts - that gut feeling. When that fits into the rule of thirds idea, I truly feel like it's something that comes pretty easily. The rules of third is a way to use composition techniques that are naturally pleasing to the eye. It's a way of using negative space in creative ways. When you place your subject on the intersection points, it really does create a more natural (and intuitive) photo.