It is believed that the Garou started the war, but the exact reason that Werewolves suddenly decided to exterminate all other changing breeds are lost to the mists of history. While many of the Fera were individually stronger spiritually and physically, they were badly outnumbered by the werewolf packs. Some of the Fera kin that the Garou concentrated upon were driven to extinction. The Ratkin were almost driven to extinction by the Garou, and one of their entire Totems was lost. Since they quite literally breed like rats, however, their numbers have recovered since then.
For a while, the Fera living in the Americas were spared, but eventually a second phase of the War of Rage was started after Colombus when European humans started expanding there. At first the Wendigo and Uktena took the side of the defending Fera in this area of the world, but when the European Garou Tribes entered the war as well, things got very complicated. The Camazotz (werebats) who had already been eraticated from Europe were finally driven to extinction in the New World as well during this time.
There was no specific end date for the end of the War of Rage, as there was no signing of a treaty or some other type of formal agreement. However, the war seemed to simmer down around the turn of the 20th century. What most likely brought the war to an end was the increased threat of the Wyrm and humanity in general to all Werecreatures and the nature they were mostly sworn to protect. The Garou Tribes eventually came to understand that their actions were wrong and many repented. By the time of Gehenna and the formation of the Tech Infantry many of the old wounds of the war had been forgotten by the Garou.
However, there were still countless victims on both sides. Some of the Fera tribes who suffered great losses have never entirely forgiven the Garou for their actions, and most of them will never forget the great tragedy of the War of Rage.