An extreme example would be Maos Great Leap Forward, where there was a human-led drive to exterminate sparrows as part of pest control, which in turn led to famines because sparrows also served as pest control for insects.

Humans are very good at introducing invasive species (domestic cat, kudzu) and pretty bad at forseeing the impact they have

I suppose I'm wondering that since domestic cats are already well introduced, perhaps removing them can also have unforeseen negative impacts to the environment!