How do we deal with something like this? Easy!
The primacy of Peter is the power of jurisdiction - not simply directive authority or of excellence or of honor - conferred by Jesus Christ on the Prince of the Apostles, by force of which he became supreme head and ruler of the whole Church.
Vatican I, defining this point of doctrine, merely interpreted authentically the words of Christ, whose historicity is admitted even by rationalists.
The primacy of Peter is insinuated in the changing of his name, PROMISED in the colloquy at Cesarea Philippi, CONFERRED after the resurrection on the banks of the Lake of Tiberias, and EXERCISED in the nascent Church.