How about I rid of a shitty cat?
That sounds cruel. What's the cat done to make you feel this way?
I am allergic to cats
It's too bad you didn't know you were allergic to cats in the first place, but since that's the case, you'll have to find him a new home.
But I need the cat so I can call in sick at work.
That's not a very good reason to keep your cat, especially when it sounds like you don't even like him. Using him to get sick days isn't ethical, either. It would be best for everyone if you would find a home for the cat where he's loved and appreciated.