"Anger and unkindness arise when people's understanding is limited. The deeper their understanding the more their anger disappears, and kindness, love and peace spread."
Rebbe Nachman of Breslov, Likutei Eitzot.
In the comments to this post, I posted the following explanation to R' Nachman's insight:
Many issues are complex. People who cannot handle the complexity will choose a simpler explanation which is absolutely correct with regards to one aspect of the issue, but incorrect with regard to other aspects.* Imagine that two people chose different understandings of an issue, each of which is correct with regard to a different aspect of the issue. Each person will refuse to accept the other's criticism of their understanding, because that would mean giving up their understanding across the board - and they KNOW, correctly, that they shouldn't do that. So each person is forced to ignore rather than consider the other's arguments. Which leads to frustration, and from there to "Anger and unkindness".
The two incomplete understandings may both be intellectual. Or, as is common in debates about religion, one is philosophical and the other emotional or intuitive. Either way, the dynamic of the debate is the same.
*A good example is politics, where liberals and conservatives are both right SOMETIMES, but (partly due to incomplete information) nobody in the world fully understands the entire issue.