The trouble with Rome

It comes down to humility.  From the very beginning, the bishop of Rome, whom we know as the pope, has always held the position of leader among equals. 
From very early on, the church of Jesus Christ has been made up of five patriarchates: Jerusalem, Antioch, Rome, Constantinople and Alexandria.  The problem developed over many centuries and finally came to a head in 1054 when the pope demanded that he take the title of Christ's vicar on earth.  In other words, he wanted authority over everyone.  He wanted all the other patriarchs to submit to him.  But their response was no, it has never been that way, that idea is an innovation and contrary to what Jesus and the apostles handed down to us.
At that point in time, the pope excommunicated the patriarch of Constantinople and the patriarch reciprocated.  There has been a rift between Rome and the other patriarchates ever since.
What it comes down to is this, the pope needs to admit the error and accept a position of equality with the other patriarchs.
But then all of the doctrinal innovations that have developed in the Roman church since then would need to be corrected.  And that would be a really big job.