This is well-covered area in TAW and it's super "Googleable," but I'd say there is no one quick explanation as to why East and West are no longer together and the West vacated the ancient faith. It isn't 'just' the filioque. It's much more. East and West were barely cohabitating for years. The West quit using leavened bread, which understandably perplexed the Orthodox. It made zero sense. Then they forced celibacy on their clergy, which was equally odd and a head-scratcher. They started to view salvation in terms of satisfaction, compensation, legalism, blood, and appeasement terminology that the East and West had never really utilized before. The East was very focused on mystery, the West very focused on juridical mindsets and the desire to EXPLAIN everything.
The big elephant in the room wasn't the unleavened bread vs. flat wafers or the celibacy or the juridical stuff, it was the PAPAL POWER ABUSES. The Popes started to claim powers, pervues, and scopes of authority they had never had previously. Popes started to intrude in the affairs of other jurisdictions, pontificate where it wasn't welcome, and the whole Photian affairs left a VERY BAD taste in the mouths of the Orthodox East. Popes claimed to be the entire church in a nutshell, and the conciliar model that served the Church so well was being trampled upon heavily.
Another sore spot was missionary activity and spreading the Word. The Roman Catholics were crossing into Orthodox lands and pushing their agendas there. Like I said, it's complicated.
But the papal claims and filioque were the biggies, the Photian issues and the other views and ways of seeing salvation all added up like sediment that had been accumulating for a long time.
The East had and still does have a much healthier, more holistic, beautiful, and true vision of God and His Church than anyone who has come since. If only I could've known the Jesus of Orthodoxy when I was a teen!!! Imagine a God-Man who suffers through death and dies like me only to descend into death, defeat it, and rise like a phoenix breathing life back into a broken human matrix! Imagine if I knew a God and a Church when I was a teen that focused not on God "creating" grace, but extending grace as a principle of WHO HE IS! Grace isn't created! It's an extension of the Godhead, participation in the divine life to save me! Imagine if I could've known a God who sees sin as missing a mark and trying to readjust my aim rather than the courtroom drama of the West! Ponder what my life might've been like back when I was younger if I had only known the fullness of the Church and not guilt-driven Law and Order episodes with Jesus portrayed as taking a bullet for me before an angry judge and jury.
Rest assured that the Orthodox Church is unchanged, unfettered, and constant. The West fell away, not the reverse, and the OC is right 100%. The Catholics and Protestants contain kernels (some kernels huge, some the size of dog kibble) of truth, while we possess the whole truckload of it.
I suggest reading about the Photian controversies. The Catholics call it "The Photian Schism," which is extremely inaccurate, because the only schism made was from the pope of that time! But the Photian situation really laid the ground work for the mushroom cloud of 1054 and the stupidity that followed.