[alt text: an illustration of a person with a head-empty expression on their face, who is saying, "Not letting your cat outside is CRUEL!" Around the person are various gruesome scenes of different cats in distress. From the top and going clockwise, the scenes include: a cat being carried away by a hawk; a cat that is on fire; a dead cat in the road that has been run over by a car; several dead kittens; a cat that is missing an eye and various patches of fur; a cat that is feasting on a songbird; and a cat that is being carried away by a coyote. The person appears to be completely oblivious to these scenes of distress.]
Humans are not an invasive species. We migrated to everywhere we currently live. Invasive species are usually defined something along the lines of being a species that was introduced somewhere (by people) where it didn't previously exist and is harmful to its new environment. We meet the harmfulness part of the definition but not the introduction part of it.