Why is weight loss/management a controversial science?

It seems there is no one RIGHT answer, no single solution.

Well, you kind of answered your own question. ;-)

It's controversial because no one method works for everyone. If there were a simple "right answer" there wouldn't be any controversy. Some people get good results with regimens that don't work at all for other people, and some weight loss plans are controversial because they are considered dangerous (overly strict limitations of certain types of nutrients, for example). Another controversy is whether or not emphasis on weight loss may lead to eating disorders. Then there are weight loss drugs, which have a spotty safety record at best.

The least controversial weight loss method (eat less and exercise) doesn't sell well on best-seller lists. But not to be flippant, the mechanism of weight loss and gain is imperfectly understood and there is definitely not a 'magic bullet' method that works for everyone.

It's not so much that it is controversial, rather weight loss is critically tied to metabolism, which is a very complicated and highly regulated set of processes that go on in the body. The right answer is to eat less calories or burn more calories - these are the only possible way to lose weight. Many diets try to regulate the way the body used energy, but since the regulation is so complicated, most people do not really understand it well. Different foods are metabolized by the body at different rates, so diets like the atkins diet try to supply the body with non-sugar energy molecules, which the body can use, though sugar metabolism is one of the most straightforward ways to get energy. The problem with sugar metabolism is that it is faster, so energy can be generated faster than the body can use it in many cases, so sugar metabolism often results in the production of fat.
The worst thing about many foods is that they are very high in fructose(high fructose corn syrup). There is nothing bad about fructose in small amounts, but in very high amounts, fructose metabolism bypasses regulatory steps that other sugars must go through, so it gets turned into energy very quickly, and since the body has too much energy it stores it, again as fat.

The big problem is that most people who talk about weight gain or loss don't really understand how metabolism really works.

For instance, if you eat nothing at all for a prolonged period, your brain still needs energy, so your body begins to metabolize fat and your own muscle protein in order to supply energy to the brain... but by degrading muscle protein which is in itself a big energy user, you lower your bodies overall energy demand in the long run, and thus even more energy gets converted to fat when you start eating again. This is why starvation diets do not work.

Also as you lose weight, your metabolism decreases since there is simply less of you that needs energy. So if you try to lose weight by dieting, you need to cut out calories, but as you lose more and more, your metabolic rate also decreases, so you need to cut out more calories to continue losing weight.

The body is much more complex than people give it credit for, and most people who try to give diet advice don't really understand what actually happens to the energy you get from food, and they especially don't understand that metabolism is by nature, very highly regulated.