When I was younger I usually went along with the advice of my parents, just to please them. Now I realize that, that sometimes I should have followed my heart instead.
I do not think they were always right.
However, parents do have more life experience than children. So I think it is smart to consider what they have to say. My Dad once gave me an advice that if I do not know what to do, ask many people
for their point of view, and make the decision based on as much information as possible. That was a good advice, I think. Since you want to become a monk, perhaps it would be a good idea to talk face-to-face with someone who followed a similar path?
Also, check the biography of Tulku Tsem Rinpoche. If I recall correctly, he also felt strongly about becoming a monk, and decided not to pursue the full length of High School. Instead, he took GED exams.
I don't remember exactly where I heard or read about it. It may have been his autobiographical video, http://www.youtube.com/watch?v=zYaBLbubmjM
So see if you could perhaps finish school, but earlier than normally required. This could be a middle ground between what your parents suggest with their loving heart, and also what you desire.
So, I think it would be wise to also talk to the school councilor. Maybe there are some options that could satisfy you and your parents.
Further, I think it's important to really inquire into how serious you are about this. Is it just a wish, or is it a passion? Sometimes our feelings deceive us into thinking that this is what we want, and later we may become disappointed. If you could talk to someone face-to-face, I'm sure they could be more insightful about this. Of course, in the end, the decision is yours.