My parents won't let me live at home anymore and it makes me angry.
What about your parents not wanting to live at home makes you angry?
I like living at home because I don't have to pay
You should get a job and move out of your parent's house once you become old enough. You need to grow up and be more responsible. You're supposed to pay your own way and be proud of your accomplishments.
I'm sorry. I know it's wrong to be living in the basement, having parents pay for everything.
Your parents' belief that you should no longer live with them now that you're of age is valid and while not all parents believe this, it's acceptable that your parents do. Once you're able to support yourself and be independent I'm sure you'll feel a great sense of pride.