Why not call her for an appointment to discuss it? That way you both get to talk, it might feel less like an attack. Cuz, why exactly are you worried about her being angry with you? How would you like it if she used the same opportunity to give you a "the last word" letter? KWIM? You might feel better to have the last word undisputed, but why should she read your letter? If i were a t, i dont think i would. What good would come of it?

Eta - what would it MEAN if you cannot convince her you are right? Does it mean you are wrong? Or does it mean she is different from you?