How do you convince your parents to let you kill yourself?

There is no possible way to convince a person who loves you, especially people who love you as deeply as your parents, to let you kill yourself. They understand your worth and love you, and want the best for you. And the best for you is to live without the want to kill yourself and without depression. Suicide is not the answer. Please listen to them, and talk to them. You should also talk to a counselor. Remember that suicide is something you can never take back and can never be undone, and your problems can be fixed.