In NC can a 16 year old move out of the home against his parent's wishes just to get away?

Not legally. honestly though it depends on your situations. cops will tell you as they have me that legally there is nothing they can do after you turn , if you run away and your parents want you home then some cops wont even listen and if they do they will only bring you home once. if you do it again then they will not bring you home because they have no obligation to