The fixed idea pretends that everything is ordered and predictable and that the unpredictable enturbulation isn't there. We of course need to find out what it is that is being kept out of existence. Because if we actually face it and resolve it, there wouldn't be much use for the fixed idea any longer. Balance - Life is most fun if there is an optimum balance between what is predictable and what isn't. It wouldn't be enjoyable to control the whole world.
Ideas usually have contrasting ideas, actions have opposition, etc.
It might be sobering if the person realizes how it would actually be if the fixed idea was absolutely true and nothing to the contrary could exist. Examples - Getting examples of the application of the fixed idea will tend to ground it more in reality, so that it can be examined. Even better, if you can get the person to come up with counter-examples, well, then the fixed idea is already freeing up. Origin - If we can examine where the fixed idea comes from, how one decided on it, or didn't decide on it, and so forth, that will tend to free it up. The idea is most powerful as a stand-alone generality.