What is the best argument against an Eastern Orthodox claim that the Roman Catholics are the ones who broke away?

Of course they say that; if they did not, they would have no basis for being Orthodox, so you have to expect that excuse. It is easily disproven. Read our book, which covers all the popes from the first century to the eighth century, at least through the first seven councils that the Orthodox themselves accept, and you are amazed at how much authority everyone from everywhere invested in the pope; it is obvious he is in control and makes the final decision, over and over, throughout that history. There was even an Orthodox writer who reviewed our book and admitted that if you are Orthodox you will have a hard time remaining so after reading it. The whole issue revolves around the papacy. Since the Orthodox do not have a papacy, they are the ones who left, because we still have the papacy, unbroken from one pope to the next, just as it was in the first eight centuries. So how can we be said to have left when we still have the papacy? Either you accept the pope or you do not, and if you do not, you are not Catholic.