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Composition is basically analogous to grammar. It's how you arrange your ideas into a structure that makes sense to the reader (or in this case, viewer).
There are some bare bones rules for composition, the same as grammar. A sentence won't make sense if the words aren't in order, and a photo won't make sense if the subject is cut in middle by the edge of the frame or obscured by another element.
There are levels of grammar that increase with literacy. It starts with a very simplistic level that children can understand, which then becomes more complex and nuanced as the reading level increases. Similarly, composition starts as a very basic concept, usually with something in the center of the frame, and the idea being expressed is just "LOOK AT THIS THING." As compositional skill improves, it might be "look at the interplay of light and shadow on this thing" or "look at how this thing counterbalances the environment" or "look at all the things in this photo."
The idea that there are hard and fast rules for composition is sort of like saying there are hard and fast rules for grammar. It's only partially true, and the true skill of an artist and writer is how deftly they can interpret and bend and manipulate the rules to their own end. Cormac McCarthy has a tenuous relationship with grammar and punctuation, yet he is one of the greatest writers of the last 100 years. Similarly, Hiroshi Sugimoto was famous for his series of photos called Seascapes, which are almost anti-composition. Leaving out commas and sloppy grammar won't make you Cormac, and centering your composition won't make you Sugimoto. There's more to it than that.
In general, when someone gives the advice to not center your subject or to put the horizon line a little higher or lower, it's because they've already read that "sentence." A centered subject is the grammatical equivalent of using the same sentence structure over and over again. Vary your sentences.
