What do you think of rehoming the elderly cat my wife and I adopted?
Why would you rehome the cat?
I feel like my wife is content with not having a child because she has the cat.
Don't rehome the cat, that would be a heartless thing to do after having adopted it. Your home will be lonely without the cat.
I get that but I want kids and cats are for people without kids.
It's unfortunate that you feel that was about the cat, but cats aren't just for people who can't have children. Cats are great pets for anyone who likes cats and can take care of them properly. If you really feel you need to rehome the cat you should talk to your wife about it.