Seligman gives a reference to a study that actually found that losing weight in overweight middle-aged men made their health worse, not better.

Three considerations:

• weight in the form of muscle is good. As you lose that you get less healthy. If you lose both 5kg of fat and 5kg of muscle at once you will probably be less healthy at the end of that adventure.
• Initially changing your bodyweight in large chunks is probably bad but in the long run, being 10kg closer to the ideal bodyweight for your size/age will be better for you. If nothing else - (from first principles) giving your heart less of a hard time pumping blood around.
• Just losing weight might throw off ratios of things like cholesterol in the body, (again) causing initial unhealthyness but later when they stabilise again you will be generally healthier.

Having not seen the study, I can't be too confident but these don't seem like outrageous explanations.