The center of gravitation is also just a simplification, or how scientists call it: "a model". Actually everything gravitates around everything else, as the article also explains.

Models, or simplifications, aren't bad though. Because what value can you get out of "everything gravitates around everything else"? Not much. But if you use a model, you can use the model to explain what happened in the past and use it to make an approximated assumption about the future. You can use it to guide decisions, and you can use it to focus on more details in other areas. E.g. if you don't use the actual trajectory of everything but a model, you can still calculate where Mars will be when you reach it if you start right now from point X on Earth. Of course the center of Mars will not be at exactly the same point, but it will be a good enough approximation that you can start planning resources required to get there, and it can help you decide if "now" and point X are good inputs to that travel plan.

Models are a good, helpful tool. They are just not explaining everything, and that on purpose, and as a human we always need to be aware of that models are just models and not reality.