One thing I struggled with was that the desire to drink continued long after I also really really wanted to stop. That duality confused me. I didn't understand how I could desperately want to be sober and crave a drink at the same time. I thought I was losing my mind.
What I learned on SR was that those two desires - the desire to be sober and the desire to drink again - come from very different parts of the brain. The desire to be sober comes from my rational, thinking frontal cortex and the desire to drink comes from my amygdaloid complex. It is altogether possible to have both of them firing at the same time, creating competing desires and mental dissonance - that battle that raged in my head that no one could see or hear but me.
To me, wanting to be sober more than you want to drink simply means putting your frontal cortex, your rational mind, in charge and telling that seemingly relentless urge to drink "NO".
It only seems relentless. It's plenty pesky, for sure, but it relents if you starve it long enough.