This myth comes from a misapplication of the “3,500 calorie rule,” the idea that every person needs to cut the same amount of calories to lose a pound, every time. By that reasoning, if I, as a 150-pound man, start taking a daily 30-minute walk at a moderate pace (which burns about 100 calories), I should lose a pound in 35 days, 10 pounds in a year. But consider the implication if that were so: In 15 years, poof! I would vanish altogether. Something is obviously wrong, but what?
For one, the numbers are estimates and vary among people. The formula also assumes no other behavior changes, but as we lose weight, we may become hungrier or move less. The formula also neglects that, as you shrink, it takes less energy to move. Eventually, the small change in calorie intake is negated.
Bottom line: Burning more calories than you take in is the only way to lose weight without surgery. But your personal equation will vary. Count what you eat and burn, and adjust to meet your goals.
So how can you determine the effects of long-term changes in calorie intake or burning? There are two free, reliable computer programs to help. They can be found here and here. Using these tools, I find that my hypothetical daily walk would actually lead to a more plausible long-term loss of 7.5 pounds, assuming I do not change my other behaviors.
You can find more information about the science behind obesity and sign up for weekly updates at obesityandenergetics.org.