I think it's just the conviction that the "problem" is very serious and the conclusion that an extreme measure is the only possible solution (due to reasoning b

I think it's just the conviction that the "problem" is very serious and the conclusion that an extreme measure is the only possible solution (due to reasoning based on incorrect or incomplete information). I guess you could call that crazy, but it's more like stupid (due to lack of sufficient research/information) and impulsive (lack of second-guessing). Anyone can fall for it imo, but for most people self-preservation overrides the will to sacrifice themselves (and others) for "the greater good". Which is what extremists are doing, believing their actions are right and the cost (incl. loss of lives) and self-sacrifice are necessary.