I learned a long time ago that sometimes it is better to be happy than to be right. Translated into college work, we may think a teacher does not hold our opinions and comments against our work, But my experience has been different.
Took a Humanities class and all my papers were A's until I wrote a paper that was contrary to the instructor's liberal feminist position. Suddenly the grade was a B and her comments were that I didn't understand what the essay was trying to convey. This happened twice on the same subject matter.
Oh I understood the essays all right but I disagreed with them. From that moment on I wrote "to the teacher" keeping in mind her stance and beliefs. Went back to getting A's on my papers. I still learned a lot but I kept my opinions to myself because she DID hold them against me.
So if grades are an important factor, keep this in mind. But if taking her on is more important keep in mind your grades may reflect it. Remember it is unlikely you will win and she is very unlikely to change her position.