Once again, you don't know the first thing about cats! How should I take them outside, on a lead? Maybe you are mixing them up with dogs?
As for loving living inside - do you never go anywhere? Actually, it wouldn't surprise me to hear that you don't. I rather suspect many posters on MN have limited social activity and try to make themselves feel important by pushing their unwanted views on random strangers online.
My oldest cat lived in a crate for three months after an injury. On the day before his last check-up with the vet I took him outside for a couple of minutes, before I had time to do anything sensible he was off, over the fence and gone.
I have also had dogs in the past, so please do not insult me by insinuating I have cats because I can't be bothered. I spend vast amounts of money on my cats, not to mention time with them, and they have the best life.
Why have you, and others, hijacked a thread where the OP was asking for help in getting her cat back? We don't actually care what people like you think, and continually telling me what I should do with my cats is falling on very deaf ears, so you might as well give up.