You cannot reason with someone that is by definition unreasonable. Attempting to do so is an exercise in futility.
Now if she's just emotional then try steering her to your point of view. Naturally you cannot argue with someone that is angry, but you can calm them down. I learned this when I was married and won close to 100% of the time using this technique I developed. I probably should patent it or something, but oh well.
I understand blah blah blah :mirror their reasoning why they're mad:. How would you feel if.... :state your perception you want her to join your side on.
Women feel before they think. This is why they're emotionally grounded and men are logically grounded. Just different ways we think and associate with others. Women emote, men fix. It's a cliche for a reason. What you need to do is get her to "feel" things from you logical perspective. The next step is to diffuse her anger/displeasure by acknowledging it and then reinforcing the solution by relating it back to her as those it was her idea and she's already accepted it as the "fit".
Example of doing it wrong:
Woman: I just can't stand my friend. She does xyz that makes me so angry. Blah blah blah.
Man: If she makes you so mad then why don't you talk to her about it?
Example of doing it right:
Woman: I just can't stand my friend. She does xyz that makes me so angry. Blah blah blah.
Man: I understand she makes you upset because she did that, but how would you feel if she made you mad doing something similar and instead of her talking to you about it she just ragged on you to all your friends. You wouldn't appreciate it would you?
Woman: No, probably not.
Man: It's okay to be angry and it's perfectly natural. But like you said you wouldn't feel very good if she did this to you and would want to talk it out instead.
Woman: Yeah, I know. I should call her.
