The third canon of this council is short and it caused centuries of trouble. It gave the bishop of Constantinople the prerogative of honour after the bishop of Rome, because Constantinople is New Rome. The reasoning is what matters. Precedence among the great sees had been justified by apostolic foundation, and Constantinople had none: it was a provincial town until an emperor rebuilt it. The canon substitutes political importance for apostolic descent.
Rome did not accept it, and the refusal was consistent. If rank followed the location of the imperial court, then Roman primacy rested on the empire rather than on Peter, and the whole basis of the Latin understanding of the papacy was at stake. The same claim was made more forcefully at Chalcedon seventy years later in its twenty-eighth canon, and Leo I annulled that canon as far as he was able, while the Eastern churches proceeded on the basis of it.
The dispute is one of the long roots of the East-West Schism, and it is worth noticing because it is not doctrinal. Nothing about God is in question. What is in question is how authority in the church is distributed and on what grounds, and the two halves of Christendom gave different answers early, kept giving them, and eventually found the difference unbridgeable.