I've always loved paradoxes and contradictions. In most arguments both sides are correct. What is incorrect is that they don't respect the correctness of the other side. Most debates are artificial and it is really a more fruitful use of your time to learn, rather than try to teach.
My old teacher Bawa Muhaiyaddeen once appeared on a radio show in San Francisco where the interviewer praised him as a great guru. Bawa denied that he was a guru and insisted he was only a student.