I once worked with a dancer who could fold forward and place her palms flat on the floor without warming up. By most measures she was remarkably flexible. She also had recurring lower back pain that no amount of stretching seemed to touch, and once we started working together, it became clear why. She had enormous range of motion and almost no control over the last third of it.
This is the distinction I keep coming back to with clients, because the two words get used interchangeably and they are not describing the same thing. Flexibility is how far a joint or a muscle can passively lengthen. Mobility is how much of that range you can actually access and control on your own, under some load, without something else compensating to get you there. You can be flexible and immobile at the same time, and in my experience that combination causes more trouble than simply being stiff.
The dancer could reach the floor because years of training had lengthened her hamstrings and back extensors well past what most bodies need. But in the last part of that range, her deep hip and core muscles were not doing anything. Nothing was actively holding or controlling that end position. Her nervous system had essentially been left unsupervised there, and unsupervised ranges of motion are, for some people, where problems accumulate.
So instead of more stretching, we spent months on control at end range. Slow, loaded movements into the same position she could already reach passively, but now with tension, now with her own muscles doing the holding instead of gravity and momentum. It was less satisfying than a deep stretch. It also did more for her back than anything she had tried before.
Flexibility asks how far you can go. Mobility asks whether you can be trusted once you get there. I do not think one is more important than the other in every case, but I do think most people have been told to chase flexibility when what they actually needed was control.
This is not a universal rule, and plenty of people are simply stiff and would benefit from more range, full stop. But before I hand anyone a stretching routine, I want to know whether their limitation is really a lack of length, or a lack of trust between their brain and a range they already have. Those two problems look similar from the outside and require almost opposite solutions.