For people who take the "it's not about willpower" approach--what exactly does that mean?

I can understand that resisting actual binge urges that happen to people with BED is not the same as it is for non-disordered people to resist the thought of eating something unhealthy, and I fully do not beat myself up for struggling to not respond to an urge in that sense--I know I'm fighting a harder battle because of my BED than the average person.

But when it comes to recovering, I've never understood what people mean by "it's not about willpower" (or discipline, self-control, etc.) I want so, so badly to recover, and I've done so much work to learn what I'm supposed to do in order to stop binging. But when it comes time to apply all that prep work--when I feel the urge and need to resist--I never manage to do it. If the missing ingredient isn't willpower, what is it? It seems to me like that's the only thing I'm missing...