When people object to this practice, they tend to raise at least one of two points: (1) objectifying or personifying the problem belies the fact that it is an "illness" and may therefore be a form of denial, and/or keep people from receiving needed treatment; and/or (2) attributing the problem to something external may be seen as a means of absolving responsibility for the consequences of the problem, or for change.
First, my response to these objections:
1) Narrative therapy is based on a philosophy called social constructionism, which basically contends that all of our perceptions of "Truth" are no more or less than ideas that we've collectively agreed upon - they are socially constructed (i.e., built). The concepts of "illness" and "treatment" are just that - constructions of our particular social location. In other parts of the world, and in other eras, the same physical symptoms that we label an illness (cancer, for instance, or seizures, or whatever) have been described quite differently, with very different interventions. When it comes to selecting among available constructions, what really matters is what leads to better outcomes in people's lives (however they define that for themselves!)
2) Construing the problem as internal - as part of the person who has the problem - tends to cause people to feel bad about themselves, and/or about the potential for change. People are actually less likely to take action to address a problem when it is seen as internal. In contrast, framing it as external creates some space for the person to maneuver - to see possibilities for change by redefining their relationship with it, and adjusting their responses to it.
Now, I'd planned to follow my response to the objections with a summary of what I see as the benefits of externalizing - but my response already captured many of them. Most notably, externalizing the problem creates room for alternatives - identifying exceptions to the problem that already exist, and taking advantages of every opportunity to subvert the problem to shape one's life in preferred directions. Part of how externalizing accomplishes this is by removing blame. If the problem is external, it's not your fault that it's there. It's only your responsibility how you choose to respond to it. In contrast, if you are the problem (whether because you "are" ill, or have a certain personality or temperament, or whatever), it's natural to feel like it's your "fault" - and all the guilt/shame/blame that accompany that assumption. While the result of "illness" or "problem-focused" constructions is often to objectify the person (a diabetic, a schizophrenic, etc), externalizing reverses this process by intentionally objectifying the problem itself. The immediate result is an improvement in self-image, including belief in one's own capacity to resist or overcome the problem.
Externalizing also offers a language to talk about, and a way to identify, the strategies the problem uses to get a hold of the person, as well as ways that the person can begin to resist - things s/he can choose (other than whether or not to have the problem, which is often not something under her/his direct control) that affect the problem and her/his relationship with it. In this way, new directions are unearthed, and preferred life circumstances begin to become a reality.
Can shifting language really accomplish all this? Yes - to the extent that the language is internalized. It helps a little to say it without believing it, but it helps a lot to actually believe it. I've seen rapid, significant change happen just from making this shift.
What do you think about externalizing problems, and narrative theory more generally?