Need? not really. In HS the parent will want want to make sure that the curriculum meets any admissions requirements, both in general (eg, meeting science or FL expectations) and in particular (eg, Math II subject test for CalTech or Calc for some CS/Engineering programs). But HS pre-reqs for specific college majors (except some CS/Eng) are pretty rare. The parent won’t need to know how the major progresses or about career center resources- that will be the student’s job to know about.
Being interested & supportive is one thing. Taking the lead in researching possible majors is another.