The New Founding Fathers of America seem surprised when The Forever Purge turns their idea against them, but the chaotic uprising was inevitable. While the Purge franchise still has yet to fully explain exactly what circumstances led the NFFA to take power and successfully institute Purge Night, at this point in the franchise, it arguably doesn't matter. Like the event itself within its own universe, the Purge franchise has become a tradition, so far producing five films and two seasons of a spinoff TV show.
While it's been eight years since the original Purge movie hit theaters and became a sleeper hit, what draws audiences to see each new Purge installment is largely the same as what drew them the first time: The Purge Night concept, a 12-hour period where all crime is legal, is an inherently interesting one that presents the possibility for countless scenarios in which both evil people and good people can shine. The fight or flight instinct is a strong one, and one never really knows what they're capable of until pushed to the brink.
Unfortunately, that's true for those twisted enough to Purge as well, and while the NFFA may have stated their goal was to offer frustrated Americans an opportunity for 12 hours of uninhibited catharsis per year, those ready to take up arms and go to slaughter are unlikely to ever satiate their blood-lust. Thus, it was only a matter of time before 12 hours of carnage a year ceased being enough for them, and the U.S. descended into violent insurrection. One need only remember The First Purge's villain "Skeletor" to figure out why.
"Unleashing the beast," as the Purge franchise dubs it, allows those with violent or sexual urges normally shunned from polite society to indulge in their deepest criminal desires. The idea that these people can exorcise their mental demons by having 12 hours a year to go nuts may sound somewhat logical, but it's one that's inherently flawed. There's a reason most violent criminals re-offend, whether they be murderers, sex offenders, or another type of terrifying human monster. To them, their need to kill, assault, or maim is a compulsion, and no matter how much they get to do it without worry, it's not going to go away.
For a pop culture example, one need only look over at Dexter, who carried around his "dark passenger." While that's a work of fiction, it's a fair enough dramatization of the urge to kill that some people hiding among the population face. It's true that not every Purger will be a murderer, but anyone participating will have likely have gotten more and more frustrated with the fact that they're always forced to stop taking part in living out their basest desires. The NFFA were holding a ticking time bomb from the very first Purge Night onward, and while they may have looked at the holiday as a way to rid society of those they deemed undesirable, the ultimate consequence of their actions in The Forever Purge was their own doom.