Here's my two cents: it's both a disorder AND a choice.
The disorder part is that when an alcoholic is triggered and gets the idea to drink, the craving starts and if you don't satisfy that craving, then all kinds of negative emotions pile on: anxiety, irritability, anger, resentment, entitlement, and depression. That doesn't happen in non-addicted people. If someone isn't addicted and you say "on second thought, let's not have that beer after all" they're like "okay, fine with me." And they don't experience distress.
But we do experience distress, so severe that drinking seems like the most reasonable way to feel better. Normal brains don't create that kind of intense emotion when a craving goes unfulfilled. Addicted brains do.
But it's also definitely a choice, because to drink is always a choice. just because you have uncomfortable emotions doesn't mean you're literally powerless to not drink. Obtaining the alcohol and going about drinking it are complex behaviors that are under our voluntary control. We don't lose control of our muscles like in a seizure, we don't lose the ability to control our arms and legs. Drinking is always a choice.
And for me, that points the way to recovery: recognizing that it is a choice, that we do have the power to say "no" to the urges. We can choose to sit with the uncomfortable emotions and tolerate them, or distract ourselves, or deal with the feelings in some way other than drinking.
So that's how I see it. The exaggerated distress that cravings cause is the "disease," but what we do with those feelings (including drinking) is a choice.