The Nicene Creed is one of the oldest official statements of the core beliefs of the Christian Church, a brief summary of the things that all Christians everywhere ought to believe as Christians. And there are two conflicting versions of it.
At issue is a key phrase that appears in the Latin version of the creed but not in the oldest Greek versions. This phrase is known as the Filioque, and you will notice that the Wikipedia entry is flagged as being under dispute. Here’s an abbreviated version of the Nicene Creed, with the Filioque clause highlighted in boldface.
We believe in one God, the Father Almighty, Maker of heaven and earth, and of all things visible and invisible. And in one Lord Jesus Christ, the only-begotten Son of God, begotten of the Father before all worlds (æons), Light of Light, very God of very God, begotten, not made, being of one substance with the Father; by whom all things were made… And in the Holy Ghost, the Lord and Giver of life, who proceedeth from the Father and the Son, who with the Father and the Son together is worshiped and glorified, who spake by the prophets…
This creed was itself the product of a controversy within the Church over whether or not Jesus was actually divine: the Arians (followers of Arius) denied his divinity, but the Trinitarians insisted that he was indeed God. As you can see from the creed above, the Trinitarians were victorious, at least within the Roman/Byzantine Empire. Arianism did not entirely go away however, and persisted most notably among the barbarian tribes threatening the Western Empire. The addition of the phrase “and the Son” may have been an attempt by the Pope in the West to emphasize the deity of Jesus, in an attempt to bring the barbarians under his sway.
Christians in the East did not see it that way, however, and were highly incensed (no pun intended) by the West’s decision to make arbitrary changes to the official dogma of the Ecumenical Council. The Filioque became a lightning rod for the power struggle that arose between the Pope in the West and the Byzantine Church in the East, eventually leading to the Great Schism. That division has endured for many centuries, despite all attempts to repair it, with little hope of reconciliation. A sad situation, to be sure, but one that was inherently unavoidable.
The problem is that, in God’s absence, the most theology can be is a bunch of guys getting together and agreeing to tell the same story. They don’t have much of an alternative: it’s not like God shows up in real life where we can observe Him and draw objective conclusions. In His absence, all men can do is sit down (much as novelists do) and try to enhance the story as it has been told thus far, with the addition of plausible-sounding details. When they all agree, the result is a story that improves with the retelling. But what happens when they disagree?
There are two possibilities. One is that there will be some kind of conflict, and one side or the other will win. This is what happened in the debate between the Arians and the Trinitarians, which the Trinitarians won. In such cases, you can assume that the victors must have had God’s blessing, and therefore their dogmas must be the correct ones. Or you could assume (with equal Biblical basis) that a Great Apostasy had occurred, and that it was the “faithful remnant” who must be correct. It’s really up to you, and each believer decides for him- or herself which assumption they prefer.
The other possible outcome is what happened with the Filioque: neither side can defeat the other, and the Church divides as a result. Each side is sure they are the true believers and the others are the apostates, but neither side can provide any objective proof for their claims, because theology is a bunch of guys getting together, in God’s absence, and embellishing the story however they see fit. Without a God Who is willing and able to show up in real life where everybody can see and hear Him, there is no objective basis for the things men say about Him, and thus no unbiased means of measuring the accuracy of men’s teachings about Him. There’s no way we can really be sure whose dogmas we ought to believe.
Then again, considering the only available source for theological doctrines, why should we believe any of it? What men invent in God’s absence is entirely coincidental to anything that may or may not be true about the God they purport to describe. And that’s why their schisms are irresolvable.