It sounds like not everyone in the group agrees there is a problem to be solved.
I share your desire for finding ways to deal with and/or resolve conflict with friends in non-authoritarian ways, but if someone were to tell me they'd rather die than engage in exploring what I see as conflict in our relationship, I'd probably spend less time with them. Maybe that's a cop-out, but I've hit my head against the wall enough times in this type of situation to make me question the value of spending my energy on something with someone who isn't interested in it.
A little piece of advice I can offer is to spend more effort finding out if the other people are interested in deeper discussion about the conflict. If they are, you have a starting point, and there are a lot of ways you could go about exploring it, talking about it, creating solutions, etc. If not, well, see my above paragraph. :)