Could it be a semantics issue? A core belief is a way of seeing ourselves and the world and just accepting it as fact, but not necessarily one that makes us feel good. In that way, it's not a choice or a non-choice; until we see it, it's not something we want to change until maybe the discomfort of it drives some people to therapy. There, it can be seen as a belief and not a rock solid truth. I see a lot of wavering in my own therapy--wanting to change, not wanting to change, afraid of change. It's interesting for me to wonder how changing my views about myself and the world changes my trajectory in life.