An Ur-Quan scout mission discovered the Dnyarri and unwillingly brought thousands of Dnyarri to the heart of the Sentient Milieu, a peaceful interplanetary organization of species. The Dnyarri used their psychic powers to dominate the minds of the Milieu. The Taalo were immune, so the Dnyarri compelled the other races of the Milieu to annihilate them. The Ur-Quan were the favored slaves of the Dnyarri, and the most susceptible to their psychic powers. The Dnyarri began to genetically experiment and separated the Brown Ur-Quan into two sub-species: the Green Ur-Quan were scientists and politicians and the Black Ur-Quan were basic soldiers and laborers. As far as anyone knows, the original Brown Ur-Quan became extinct.
Over thousands of years, the Dnyarri eventually became lax in their mental domination. A green Ur-Quan scientist named Kzer-Za noticed that the Dnyarri "detached" psychic control from an Ur-Quan suffering near-lethal pain. Using one of the few moments of mental freedom the Dnyarri gave their slaves, he injected his body with a lethal and painful poison, and used the mental freedom to broadcast the news across the empire. Dnyarri slaves everywhere began burning themselves and hacking their own bodies to give them the freedom needed to kill the nearest Dnyarri. This was refined into a brain implant known as an Excruciator which causes enough pain to force a Dnyarri to detach, but leaves the Ur-Quan's body whole and functional.
Now free, the Ur-Quan decided that extinction was too good for the Dnyarri. Instead the Dnyarri were genetically modified into dumb "Talking Pets", retaining psychic powers only to allow translation and communication with alien species, something the Ur-Quan now considered demeaning. The two sub-species of the Ur-Quan developed doctrines to ensure they would not be slaves again. The green Ur-Quan, renamed the Ur-Quan Kzer-Za in honor of the scientist who freed them, devised the "Path of Now and Forever", which states that all non-Ur-Quan sentient life be slaves to the Ur-Quan either as battle thralls, or forever be imprisoned on their homeworlds under impenetrable force-fields. The Black Ur-Quan, renamed the Ur-Quan Kohr-Ah after their new leader, felt that only their "Eternal Doctrine", the annihilation of non-Ur-Quan life, would keep them safe from slavery. This led to a war between the Kohr-Ah and the Kzer-Za known as The Doctrinal Conflict, which devastated both sides. The Kzer-Za eventually triumphed through the discovery of an enormous Precursor Battleship named the Sa-Matra. Defeated, the Kohr-Ah were sent in the opposite direction of the galaxy as the Kzer-Za, with the understanding that when the two species met again, they would fight The Doctrinal Conflict once more, with the victor claiming the Sa-Matra.
That second Doctrinal Conflict is ongoing during the Star Control 2. You can't but help feel sympathy towards the two brother races, seeing as a single live Dnyarri, restored to full health, is at the moment enslaving an entire race called the Umgah. So really, the Ur-Quan just don't want to be slaves any more, having experienced the cruetly of a psychic master-race, and to be honest their treatment of their slave races and battle thralls is quite fair and surprisingly benevolent. Some races, such as the Spathi, even welcomed the chance to live under a permanent and unpenetrable shield, free from the worries (and dangers) of the galaxy.