The Great Refusal. Back in the day, the Free Council was just a collection of Apostate mages calling themselves the Nameless, who didn't care for either the Pentacle Orders or the Seers of the Throne, instead focusing on implementing modern mortal ideas in the study of magic. However, at the beginning of the 20th century, the Seers approached the Nameless, asking them to join together against the Diamond Orders so they could hoard all the magical power for themselves. The Nameless reacted poorly, as the name suggests, slaughtering large numbers of Seers and formally aligning with the Pentacle Orders by declaring themselves a new mage Order.
All the other Diamond Orders were having extreme doubts about the Nameless Orders, and in places were actually preparing to fight with them. Then, at the eleventh hour, the Silver Ladder - the people who, theoretically, should be the Free Council's greatest ideological rivals - sends a message to all corners of the Earth: Accept the Free Council as allies. Help them fight the Seers.
Not only that, but this conflict crippled the Hegemonic Ministry, weakening them to such a degree they are still having a hard time recovering nowadays.
You can say whatever you want about the Exarchs, and you're probably right to boot, but know that they broke reality's spine and bend it to their will, know that they killed and enslaved gods, know that they have been grinding down humanity since time immemorial, know that they have won. Truly, truly, won and mankind has payed for their hubris forever since.