They called it the Curse of the Eva, but the people knew better. It wasn't the Eva that presented the Curse, it was the LCL.
LCL was a liquefied oxygen meant to fill your lungs and oxygenate your blood from within. When the Angel Wars ended, the Evangelion program was disbanded, and the corporation WILLE decided to dispose of the LCL without any further research into its use.
But that's where things started getting complicated.
The first attack came three years after the disbandment. Hordes of people swarmed WILLE's base of operations, chanting words in a strange language, and calling for LCL. Word soon spread that the attackers were biting people, drinking their blood. The satisfied ones would leave the base, lips stained crimson, while the others continued their attack with rudimentary weapons crafted from whatever they could find.
The pilots of the Evangelion, though, were not included amongst the hordes of people. The thought of using the decommissioned Evas to help disperse the attack came from Dr. Akagi, but it was quickly shot down. Instead, WILLE's security force, armed with gas grenades and rubber bullets, were tasked with the clearing.