The Great Schism has a date, and the date is the least useful thing about it. In July 1054 a papal legation and the patriarch of Constantinople excommunicated one another. Both excommunications were personal rather than corporate, the pope who sent the legates was already dead, and ordinary Greeks and Latins went on communicating with each other for a long time afterwards. What 1054 marks is a convenient point on a curve, not a break.
The substance beneath it was accumulating for centuries. The filioque, the Latin insertion into the Nicene Creed of the words and the Son, describing the procession of the Holy Spirit, was objectionable to the East on two counts, one theological and one procedural. Theologically it seemed to displace the Father as the single source within the Godhead. Procedurally, and this is the argument Orthodox writers press hardest, the creed was the work of an ecumenical council and no single see had authority to alter it. Alongside that ran the growing Roman claim to jurisdiction rather than honour, disputes over married clergy, leavened or unleavened bread, and the political reality of an empire that no longer held both halves.
What actually made the division permanent came later. The Fourth Crusade sacked Constantinople in 1204, installed a Latin patriarch and looted the city for relics, and the memory of it outlasted every theological argument. Reunion councils at Lyons in 1274 and Florence in 1439 both produced signed agreements; both were repudiated by the Orthodox faithful and clergy once the delegates went home. The excommunications of 1054 were finally lifted in 1965. Communion was not restored.