Why do photographers, and photographers alone, so love these rules which tell you where to put the subject?
Texts on painting are surprisingly silent on the entire topic of the subject. Not only do they decline to tell you were to put the subject, they don't even really talk about the subject. They talk about dominant shapes and subordinate ones, and things like that, but there often is no talk of subject per se. Of course this picture is of a teapot, but it's not that the teapot is more important than anything else. Unimportant things are left out of a painting entirely.
Photographers are stuck with whatever is in the frame at the moment the shutter is pressed. This leads many, perhaps most, to view the problem as one of minimizing the unimportant and maximizing the important - the subject. The problem becomes one of getting close enough to isolate the subject, or using depth of field to accomplish the same thing. We want to hide or minimize the stuff that doesn't work.
Even when there is no subject, photographers tend to be subject-obsessed. They will invent a subject. A beautiful seascape with the sun setting in the background, and a beach, and a lighthouse, and the waves crashing, and the birds flying. There's the bloody sun, bang one third of the way down from the top, one third of the way in from the right. It's not the subject in any meaningful way, but the photographer can't push the shutter button without something on the intersection of gridlines, so there it is. If you're really lucky, the photographer has zoomed in or out so as to place the last beach umbrella on the opposing intersecting gridline, and now we've taken something beautiful and turned it into a shitty cliché.
Thanks, rule of thirds.
As long as we view the problem of making a picture this way, we're hampered. Good pictures can be made this way, to be sure. Many pictures we haven't got a choice, anyways. Professionals work with what's there, when you're taking snapshots of the kids, the kids are where they are.
Really good photos, though, are like paintings. Everything in the frame pulls together. Nothing is unimportant. Nothing can be added or removed without damaging the picture. Henri Cartier-Bresson's genius was to be able to pull more or less complete "paintings" right out of the world, albeit perhaps one attempt in 100 or 1000, but he could do it. Seemingly random elements, the trash in the street, are important but subordinate in a really good Cartier-Bresson picture.
Forget about the subject, think about the frame, what's in it and how it works together to create balance and unity, variety and interest.
Once you forget about the subject, you no longer care where to put it. The rule of thirds and all its stupid little friends don't matter any more. They vanish like dreams.