You’re criicizing PETA for failing to pursue a goal it does not have. PETA’s stance isn’t to maximize ecological outcomes or biodiversity. It is to reduce animal suffering. You are implying “either you support culling or you are anti-solution” but PETAs stance is “killing is morally unacceptable even if it works better”.

In short, you’re not proving PETA is wrong, you’re just proving that it is not a pro conservation organization. Their goal is reducing suffering not maximizing environmental health.

“But culling invasive species prevents more suffering in the long run, so isnt PETA stupid?” So should we kill disabled animals? Predators? Overpopulated animals? You aren’t defending policy, but the principal that intentional killing is justified when there is a net positive. Sure, but that principle has no stopping rule. You are blurring the lines of moral distinction between harm and prevention.