I can't give two ****s about convincing her. I totally understand when someone is very emotional and closed to logical discussion and I mostly leave it at that, but I will have that conversation with them. There are no "forbidden topics" or ones "you don't touch" with women. I touch what I wanna touch, no matter what. She wants to leave? Leave.
Women in your life will either see you as a master of reason and as a leader or they will **** test you every moment and not let you hang out in peace and will make fights and drama over nothing.
If you do not train her to become less emotional and know who she's talking to, she will spill out her guts almost in any situation where she can and feels like because by default, they don't respect you. The grow respect for you depending on how you handle their misbehaviours and the arguments you guys have and she will make sure to have arguments with you anytime she doubts your value and integrity and spine as a man. If she senses a strong spine since the beginning, she will make few to no fights. Men with a backbone are rare nowadays and no matter how emotional women are, they know when they find a good man who has his own beliefs and will not bend anytime she feels like it.