The creed the whole church confesses was agreed at Constantinople in 381. On the Holy Spirit it says: "who proceeds from the Father." The Western church, over centuries, added two words, in Latin one word, Filioque, so that it read "from the Father and the Son." That addition is the single most cited doctrinal cause of the break between Rome and the Orthodox East, and it is genuinely two quarrels wearing one name.
The quarrel about authority. An ecumenical council had set the creed and forbidden its alteration. The clause was inserted first in Spain, at Toledo in 589, spread through the Frankish realm, and was resisted at Rome itself for centuries, Pope Leo III had the original text engraved on silver shields and set up in St Peter's precisely to hold the line, before Rome finally accepted it around 1014. To the East the point was constitutional: no local church, not even Rome, may edit the common faith on its own authority. Even a true statement, added this way, is added illegitimately.
The quarrel about the Trinity. Behind the procedure lies a real theological difference. The East holds that the Father alone is the source within the Godhead, the "monarchy" of the Father, and that saying the Spirit proceeds from the Father and the Son gives the Spirit two origins and subordinates or confuses the persons. The West answers that the double procession guards the full divinity of the Son and expresses the mutual relations of the three, and that it makes explicit what the faith already held.
The bridge that keeps being rebuilt. There is an old mediating formula: the Spirit proceeds from the Father through the Son. Maximus the Confessor argued in the seventh century that this is all the Latins ever meant, and that read so, the clause is orthodox. Modern Catholic-Orthodox dialogue has returned to exactly this ground, some parties concluding that the Greek and Latin traditions may be confessing one faith in two idioms, the Greek reserving "procession" for the Spirit's ultimate origin in the Father, the Latin using it more broadly.
The dispute is not settled. Photius made it a formal charge against Rome in the ninth century; it was central to the mutual excommunications of 1054 and to the failure of the reunion councils of Lyon and Florence. But it has narrowed. When the creed is recited in Catholic-Orthodox settings today it is often said, pointedly, in its original 381 form, without the word that divided the church.