It's a weird concept, right? We can tell if someone's body is flexible if they can master gymnastics or yoga, but how do we know if their mind is flexible?
I find it easier to identify when someone's thinking is NOT flexible - in other words, when it's rigid. Rigid thinking is fixed - it doesn't adjust to accommodate new or conflicting information. It assumes universality - that there is only one accurate way to view things. Other perspectives are only considered in order to refute them.
Taking this as a reference point, then, flexible thinking actively considers alternative perspectives - not just to oppose them, but to really consider them as possibilities. Instead of insisting on one Right Answer, flexible thinking recognizes that there can be multiple truths, and they can change over time - that much of what we collectively identify as truth is simply our current best guess, and by nature provisional. As a result, new and sometimes contradictory information is welcomed.
So why is flexible thinking such an important goal of treatment? Well, for one thing, it tends to be more accurate simply because it considers contradictory information and alternate viewpoints. It also leads to innovation - new scientific discoveries and creative or technical inventions don't come from rigid thinking! On the other hand, rigid thinking tends to cause emotional pain - for example, most depression, anxiety, and self-harm are fueled by fixed beliefs about self, others, the world, and/or the future.
The good news is that flexible thinking can be learned (actually, per Piaget, it has to be learned, since it requires abstract reasoning skills). How therapists help clients develop more flexible thinking varies depending on the approach. Modeling, examining the evidence, noticing patterns, working through underlying conflicts.... How do you approach it?