You can just lure them inside with wet food!

We saw this absolutely SCRUNGLY little thing with a paw on our back door, but she bolted when she saw us. I lured her out of hiding with some wet food and a bowl, giving her small amounts at a time and gradually moving it closer to our back porch. She was entirely too young and hungry to be outside (she ate 2 whole cans of wet food at once. Even our fattest of cats are satisfied with one), so we made a plan to trap her. The trap turned out to not be necessary as she got bold after a week and let me sit with her and even pet her a bit! She did get startled and slash me up a little bit (rabies shots are ASS) but she is a sweetheart. Since she kept coming to the door we decided to quarantine our other cats and open it and lure her in with food. It eventually worked and we have her quarantined in the bathroom for now. Sadly we already have 5 cats and their politics are already complicated enough, but we found her a forever home with someone who will spoil her rotten.
Keeping animals inside is cruel. Animals should be free, or at least be able to go outside a LOT, especially cats.
Anything else is just your selfish control over another living being. You don't deserve that. And using the predator argument is stupid because you don't give a fuck about the birds and mice. You just use that argument to justify your ownership and control over the cat. The truth is you'd rather keep it inside than giving it the chance to run the fuck away from you. If you care about not having "another predator" outside, go vegan and save the hundreds or even thousands that were raised in cages and murdered for your enjoyment. Because that's what I'm doing.
Plus, a cat that hunts for enjoyment is a product of the bad parenting of their human guardians. It's a lot more common in cats that are neglected and almost non existent in cats that are cared for a lot. It's a difference of weekly vs every few years.
If you are scared about your cat being ran over by a car, you shouldn't be having a cat because it implies you live in an area that is too dangerous for them anyways.
Don't imprison your cat. It's awful. Stop being selfish and respect the animals by allowing them to be free.
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