Throughout most of the Halo series, the Covenant Empire has served as prominent fan-favorite antagonists. Their willingness to annihilate all of humanity made them a terrifying and seemingly unstoppable foe for most of the war. But since the Covenant consisted of multiple alien species, why did they suddenly seek total destruction of humanity? Why would they start a war that devastated both sides?
The reasons are complex and largely have to do with what the Covenant was founded on. The Covenant as fans know it was founded thousands of years ago by the Prophets (San'Shyuum), who discovered highly advanced Forerunner technology on their home world and reverse engineered it into technology. Eventually, they encountered the Elites (Sangheili), who, after being conquered, joined the Prophets and formed the Covenant.
Over time, the Covenant would conquer and absorb six more alien civilizations: the Hunters (Mgalekgolo), Drones (Yanme'e), Jackals (Kig-Yar), Brutes (Jiralhanae), Grunts (Unggoy) and Engineers (Huragok). The Prophets took the role of the highest echelons of their Empire's power structure, the most powerful being a Hierarch. They also instituted a caste system upon the other races, with the Elites being the second highest, until the very bottom consisted of slave races.
Covenant culture and religion are based around the worship and reverence of the Forerunners, who they see as once living gods that achieved a higher plane of existence. Due to misinterpretation from recovered artifacts, the Prophets believed that the activation of the Halo Rings as a means of transcendence -- which they'd come to refer to as the Great Journey. This religion taught by the Prophets became integral to Covenant society, where their service will one day reward them with salvation.
In 2525, a small Covenant ship using a device known as a luminary happened upon the UNSC colony world of Harvest where they detected what was thought to be thousands of Forerunner artifacts on the planet. They also detected a functioning Monitor, which they referred to as Oracles, called 032 Mendicant Bias. After recovering the Monitor and sending it back to the Covenant, the lone ship began raiding human civilian freighters.
This drew the attention of the UNSC, who believed pirates or insurrectionists were responsible. When the marine strike team led by Sargent Avery Johnson discovered it was in fact aliens who were responsible, a short skirmish erupted. At first, representatives of both the Covenant and UNSC met on Harvest’s surface for negotiations, though the Covenant simply wished to conquer humanity as they'd done with every other civilization they encountered before, and the battle for Harvest commenced.
Meanwhile, back on the Covenant's mobile capital of High Charity, the Prophets managed to activate Mendicant Bias who informed them that their interpretations of the Forerunners and the Rings were false. The Luminary didn't detect Forerunner artifacts on Harvest, but rather the human colonists. The Monitor called them Reclaimers, explaining that they were the true heirs to the Forerunners.
The Prophets realized this revelation could threaten the foundation of the entire Covenant and their rule over it. They deactivated the Monitor and decided to keep what they learned a secret by ensuring that there were no living Forerunners left in the galaxy. To prevent the rest of the Covenant from ever discovering the truth, they started the Human-Covenant War. With their superior technology and numbers, the Covenant won most engagements against the UNSC, putting them on the defensive. The war dragged on for over 28 years, during which the Covenant took or glassed hundreds of worlds, killing tens of billions of humans.
Despite this, a growing number of Elites and other species in the Covenant admired humanity's abilities and tenacity in battle, with many fearing the legendary Spartan super soldiers who could defeat scores of Covenant singlehandedly. Many began wondering why the Prophets would not consider offering humanity a place in the Covenant in exchange for surrender. This festering rebellion finally reached its peak after the events of Installation 04, which was destroyed by the Master Chief despite Covenant Commander Thel Vadam's best efforts.
Thel Vadam was punished by the Council for his failure, but was allowed to live in exchange for becoming the new Arbiter to directly serve the Hierarchs. With the Elites recent failures and their growing distrust of the Prophet's teachings and authority, the Prophet of Truth sought to replace them as the Covenant military's commanders with the Brutes, who proved much easier to manipulate.
It was also during this time that the Arbiter learned the truth of the Rings, the Forerunners and Flood from the Gravemind and 343 Guilty Spark. This would lead to a destructive civil war within the Covenant known as the Great Schism, with the majority of the Elites rebelling and joining the human’s side in the final months of the war.
During the subsequent battles for Earth and the Ark, the combined UNSC and Elite Separatist forces destroyed the last of the Covenant Loyalists and the Prophet of Truth before they could activate the Halo Array. Afterwards, the war was considered officially over, with the Arbiter signing a peace treaty with the intent of peaceful coexistence with humanity and both sides working to recover after nearly 30 years of fighting.
Though the Covenant was destroyed, splinter factions rose, intent on continuing to fight humanity. Their reasons ranged from still worshiping the Forerunners and regarding humans as affronts to their gods, while others simply feared humanity would seek revenge for atrocities committed during the war. However, none could reach the level of power the Covenant once had and were regarded mostly as a nuisance.