It's going to be one of those things that will always be a knee jerk reaction. Like how you can explain why cats shouldn't be outdoors.
They're responsible for 1/4th of the contemporary extinctions of other species. There's diseases like Rabies, FIV, FCV, Herpes, Chlamydia, FIP... There's cars/coyotes/whatever threats to life. They're invasive.
It's always "My cat would never" or "Well he cries....". "She'll scratch/pee on the furniture". "It's cruel to lock him up inside"
And weirdly, while yes, invasive reptiles have been at least partly responsible for threatening species in areas where they've settled in they're looked at as a nuisance while feral cats are just kinda there with no problems.
Cats are also at least part of the zoonotic disease vectors we have for things like plague, toxo and cat scratch fever... but rats get blamed for more than that too.