If your parents actually file to evict you in court, you might ask the court about going to mediation to see if a neutral party can help you and your parents resolve your differences.
Answer Applies to: Colorado
I suspect that there is more going on here than meets the eye. But, the answer to your question is "yes", they can evict you. Have you suggested that you either with or without them go for counseling?
Answer Applies to: New York
You are a legal adult and cannot rely on your parents for support. Perhaps if you get a job, make plans for the future and show your parents you are on the right path they will allow you to stay. Offer to pay them rent from your job. If you want to have the life you desire, it will not be handed to you.
Answer Applies to: California
If you are over 18, your parents have no legal responsibility to allow you to live in their house. So, you may not have any great options available outside of trying to work things out with your parents. This would ultimately be governed by state law, so it may good to discuss your options with a local attorney.
Answer Applies to: Illinois