So far as I am aware the main group - at least the one I most frequently encounter - that claims to "own" logic are believers - the Presuppositionalists.
If I criticise a believers arguments for being illogical it is because they are.
I could point to a particularly illogical believer who insisted that what I said was wrong because he didn't like what he thought I'd said. This beleiver continued on and on in this irrational vein despite every attempt to correct him. If you really wanted to stop believers being thought of as irrational and emotional then you want to correct behaviour like that.