Think of something you know really, really well--something you have spent a lifetime studying. Have you ever had somebody completely new to your domain try to make a statement that you knew was wrong? How did you feel and react? Even if you are kind and simply state, "well, that's an interesting opinion, but it simply isn't true. I've studied this my whole life, and the data does not support your opinion." That could be seen as arrogance, but it's really just you being confident that you know the truth and have the data to back you up.