I believe that means if they are enrolled and are thus practicing truancy. I'm asking if they can de-enroll.
A MINOR cannot un-enroll; a parent/guardian signature is required for minors.
I say this as someone who has unrolled my child from a public high school in New York state this fall. My district's "Transfer or Withdrawal Notice" requires the signature of a parent/guardian.
I think you’re referring to the right of parents have over minors to do pretty much anything to them to do pretty much anything that they want. However, parents cannot get legal assistance to keep their child in school any more than they can get legal assistance to force their child to clean their room. Some legal resources misleadingly state that they can force children to attend school with legal assistance, but that’s talking about truancy and not whether you can de-enroll in the first place.
And, once again, according the official site for New York courts, nycourt.gov , you are WRONG.
Parents can file a PINs petition with the court. Included among the reasons for a PINs petition is the minor child not attending school.
If your custodial parent is against you dropping out, they can file a PINs petition if you refuse to go to school. Since the vast majority of Family Court judges in NY have completed high school, college, and beyond, they are inclined to agree with the parent that attending school is a reasonable expectation. Your recalcitrance will be viewed negatively.
Family Court is run by ADULTS. You would have to convince ADULTS that quitting school is the best option for you. Since you have no special skills, and would not be self supporting, you will not convince intelligent adults that quitting school is a good idea.