The way I see it:
It doesn't make sense. They could theoretically just kill everyone. But if they did this, they wouldn't be anti-spirals - because their fundamental neurosis is the inability to reconcile the two facts that: the world they love was made from and runs on "evolution", and that "evolution" will eventually kill it.
Their entire arc is a contradictory revolt against this unpreventable reality.
Ultimately, although they preach self denial, they are in fact doing their hardest to maintain themselves and their preferred state of things. What they want is an endless reproduction of the same, to completely and definitively chain the future to the present. They are futilely try to prevent time itself from moving in desperation to not give way to the new. Because "evolution" is in fact death of what now exists.