There may be a confusion : whatit is wrong is to say that the Earth is the centre of the Universe, that is, the (unique) point from which the Universe is to be (fundamentally) described (the fact that the Sun turns around the Earth is only a consequence of this) ; what actually matters is that there is no centre of the Universe : there is no such point ; the description of the Universe from any point is equivalent to the description of the Universe from any other (then you are allowed to describe motions either from the Earth or from the Sun).
Mathematically, in classical mechanics, the Universe is said to be an affineaffine space.