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The argument of the paper is that an instability may happen in which the pre-flare state, with two flux systems, can have a higher energy than the post-flare state in which one of them has partially erupted. The calculation makes use of a Gold-Hoyle flux rope. I am suspicious of it because it shows, in a cartoonish sort of way, that the current penetrating the photosphere has suddenly dropped to zero during the instability. This should really be a no-no, shouldn't it? The twist cannot disappear rapidly into the solar interior because of the low Alfven speed there.
August 6, 2006