Fr. Francis Dvornik, a Roman Catholic historian says the following:
(The Greeks believe) St. Andrew was the first to be invited by the Lord to join Him, and because he had introduced his brother Peter to the Master, he, Andrew, should be regarded as the first of the Apostles, and his successors in Byzantium at least equal, if not superior, to the successors of Peter in Rome.
If this could be verified, it would amount to a clear negation of Roman primacy in the Church by the Byzantines.
Fr. says that this is merely a medieval legend made by Constantinople to get on more level footing with Rome in apostolic succession.
I’m not seeing the connection between being first = primacy, but this seems to be something people use as an argument.
Even if the Greek church really was founded by Andrew, would that mean he has primacy over Peter simply because he was the first disciple Jesus called?