My idea is that in the Golden age of technology humans started messing with DNA and cyber technology; there was a mishap with a form of Recombinant rDNA and the Hive were created. An outbreak at a secret human lab on the moon ensued and all hell broke loose. The rDNA is so powerful that it can also affect alien life forms like the Fallen and Cabal. Humans then created the Vexx to go back in time to try and exterminate the Hive threat or destroy the rDNA but there was a mishap during time travel and they became self aware? We now need to repair the Vexx for their true purpose. I noticed that one of the chained bosses in Bungie’s short Moon vid had glowing armbands. I would suggest that they would be the source of his power. Target those first Guardians.
Another idea could be that the secret 5th race created the Hive as cannon fodder to clear worlds of life so they could colonize.