Since you are an adult, moving out is your choice. Do it and make no excuses. It's hard!!! Take the cat. I don't feel that you need to apologize or explain either. Your Mom is just using the cat as leverage, and you're letting her, by worrying. If you can make it on your own by all means do so and start repairing your life from people that only want to control you. I wish you all the best.