Yesterday, I wrote this post about persuasion. The second item I included in there was empathy. Empathy is how you approach the person you are trying to persuade in order to understand their viewpoint and see if it is even possible to persuade them. Determining they are not persuadable is itself an act of empathy.
I’ve written a few posts in the past about empathy that might be helpful to give a perspective on a number of different types of empathy: