From what I understand the best way to show her your side is to avoid arguing with her. If you are right on the subject but attack her on it she goes into a defensive mode and attacks you back. As long as she's focusing on you fighting her she can't look at herself and see why she may be wrong.

So in a way by trying to tell her why she's wrong you just stick her in the mindset that's she's right.

Accept what is, let go of what was, and have faith in what will be