We look at mutants and see cool powers, but mutants in the Marvel universe are first and foremost a hated minority. Storm wants to fight the very idea of the cure, because if the cure exists - mutants will be forced to take it. The poster boy of the cure in that movie was was Warren Worthington III, and he got one of the relatively good mutations (yes, it's physically visible, but it's not one of the grotesque ones) but his father still tried to force the cure on him.
It sucks for mutants like Rogue who really do want to get rid of their powers, but mutantkind as a whole does not have the luxury of allowing the cure to exist.