Generally, a 16-year-old cannot unilaterally withdraw from school to transfer to another. While the specific rules vary by state and sometimes even by school district, minors typically need parental or guardian consent to withdraw from school. The new school may also have its own requirements for enrollment, which could include transcripts and proof of withdrawal from the previous school.
Therefore, the 16-year-old would need to involve their parents or guardians in the process. The parents or guardians would need to formally withdraw the student from the current school and then enroll them in the new school.