Only problem: this doesn't work. As anyone who either is, or knows someone who is, fat or thin and tried to lose or gain weight knows, `naturally thin' people can eat `all they want' and never gain and ounce, while `naturally fat' people can't keep their weight down longer than about five years.
Maybe you think the former cases -- the thin people -- just have a high metabolism, and the latter cases just are `psychologically weak'. Fat = psychologically weak is certainly a popular narrative in our culture. But that's an odd asymmetry: thin people are thin for physiological reasons, but fat people are fat for psychological reasons. And the `high metabolism' explanation doesn't work for thin people anyways -- just factor the metabolic rate or an estimate thereof into the calculation of the number of calories burned a day. Likewise with a `low metabolism' explanation for fat people. You'll see the same thing.
No, something is wrong in the line of thought above. And that something is the assumption that there's this number, called the average number of calories burned a day.
Now, in trying to calculate this number, of course you have to look over a period of time (previous week? previous one year? previous ten years?), and throw out exceptional days (that day you went on the 12 mile hike on Mt. Rainier, and that week you were too sick with the flu to do much more than shuffle to the bathroom and back). This requires making choices about what data to include and exclude, and these will be arbitrary but make a difference. If that's what I meant, then the easy reply would be to point out that this difference will, most likely, be negligible, or utterly irrelevant to the process by which you actually calculate your average number of calories burned a day (that is, by carrying around a little journal on a `normal day' and making note of what you do, how often you do it, and for how long).
So that's not what I mean. The average number business is confusing, so let's drop it. What we really assume when we assume there is such a thing as the average number of calories burned a day is that metabolic rate is roughly constant from day to day. Again, some daily variation is likely and expected, but typically things will stay within a fairly narrow range.
In particular, the line of thought from the first paragraph needs to assume that the metabolic rate is roughly the same for a given individual both when they are fat and when they are thin.
And this assumption was pretty thoroughly debunked. Nearly fifty years ago.
There is a reason that fat people cannot stay thin after they diet and that thin people cannot stay fat when they force themselves to gain weight. The body's metabolism speeds up or slows down to keep weight within a narrow range. Gain weight and the metabolism can as much as double; lose weight and it can slow to half its original speed.
You might still think the counting-calories method would work -- we just need to be able to measure the change in metabolism. But the change in metabolism isn't the only effect of dramatic weight loss.
fat people who lost large amounts of weight might look like someone who was never fat, but they were very different. In fact, by every metabolic measurement, they seemed like people who were starving.
Before the diet began, the fat subjects' metabolism was normal - the number of calories burned per square meter of body surface was no different from that of people who had never been fat. But when they lost weight, they were burning as much as 24 percent fewer calories per square meter of their surface area than the calories consumed by those who were naturally thin.
The Rockefeller subjects also had a psychiatric syndrome, called semi-starvation neurosis, which had been noticed before in people of normal weight who had been starved. They dreamed of food, they fantasized about food or about breaking their diet. They were anxious and depressed; some had thoughts of suicide. They secreted food in their rooms. And they binged.
The Rockefeller researchers explained their observations in one of their papers: "It is entirely possible that weight reduction, instead of resulting in a normal state for obese patients, results in an abnormal state resembling that of starved nonobese individuals."
This doesn't formally refute the line of thought from the beginning of the post: if you're fat you can lose weight by carefully monitoring caloric intake. And literally starving yourself. So the `fallacy' of the title is more polemical than logical. Still, this is a case of the `cure' being orders of magnitude worse than the `disease'.