There’s nothing so powerful in derailing an argument than to agree with the person who is arguing with you. I wonder what would happen if you quietly and calmly, in the most mature way possible, agreed with your folks that, yes, something is wrong with you and you want to fix it. Then ask that they please find a therapist. If they treat the request rudely, just repeat that you agree and want to try to change. It may be hard to keep your cool. But, as you already know, adding your rudeness to their rudeness doesn’t get you anywhere.
You might ask your school guidance counselor or your doctor to give you the names of some local therapists who work with adolescents. Once you get started, your therapist might ask that your parents join you for a few sessions. I encourage that. It will be harder to hold onto any changes you make if you go home to the same situation every day.
I wish you well.