Some responses to crisis rhetoric are sticky. The real value of a fat consciousness is in itself rather than fitting in and making fat acceptance safe for everyone.
The cry of "but you're unhealthy" is often the response to any challenge to the mindless urge to be punitive. That is then answered with 'proof' that we aren't and so on back and forth. Not only is this use of the term dubious, 'unhealthiness' lends itself no more to legitimizing hatred and prejudice than any other non threatening state.
I've never before heard this use of the term "unhealthy" before. People used to feel unwell, they were usually in bed or in hospital, they were said to be not well or healthy. If people had a chronic complaint/disability, that's what they had, their health took that into account.
Certain things or behaviours were not healthy or good for you.
The closest to this term before ironically was an almost moralistic/spiritual use "So and so has an unhealthy effect on others." But the idea of calling someone "unhealthy" as a constant chronic prognosis, or motivator or whatever is more nebulous than you'd think. And I've never cared for it or to defend myself against it.
Those who use it, who ever they are sound desperate and silly and like they are trying to sound really definitive when they aren't.