Transferring to a better high school but assistant principle won't let me?

If the school is within the district you are living the principle has no right to keep you within their school. The transfer of a child from one school to the next is the parents decision. Initially what the principle is doing holding you back is illegal. I think your family should look into why the principle is refusing transfer or bring it up with the superintendent? I can't give too much information because I don't know the entire situation. Best of luck on the transfer.