Part of the appeal of the acute model is that it offers a narrative of permanent transformation. There are two concerns about the disease model that I hear over and over again that contribute to stigma.
The first concerns personal responsibility--that if we accept the disease model and destigmatize addiction, we're letting people off the hook for bad decisions. This concern focuses on behavior prior to recovery and the chronic model offers nothing new to address these concerns.
The second concern is that addicts and alcoholics don't change and that recovery either isn't a realistic possibility for most addicts or that recovery doesn't mean what advocates say it means. Some argue that alcoholics will never really quit, others might argue that the real problem is character and when you sober up a drunken horse thief you still have a sober horse thief. This fear of recidivism (or the expected persistence of anti-social behavior that's attributed to all addicts) contributes to disease model resistance and stigma. The acute model's narrative of permanent transformation, offers a (too often false) response to this fear. The chronic model's emphasis on lifelong vulnerability contributes to these fears that recovery is temporary and unstable.
Some will invest a lot of time in micro-examining word usage to improve "messaging". I don't think that this is the answer. I believe the problem is that our message is incomplete. What we say about the illness of addiction isn't the problem. The problem is that we have very little to say about recovery.