Poll: Someone is insecure in their beliefs when they refuse to discuss/argue anything that may challenge them.
Doesn't matter what the beliefs are. It could just be your opinion of an anime character that you really, really like. Or really, really hate. Whatever. Just imagine broaching a subject with someone who does whatever they can to avoid it, even though they have all of the time and opportunity to participate. (Because it would be another thing entirely if they were busy and/or preoccupied at the time.)
What brought this on? I've run into a few cowards lately, and their irrational stupidity bugs me. So, now, I bug you. Ha!