The theory side of the LCHF diet

The idea is to give a hint of why the diet works. I am no doctor, therefore this post is sort of a concoction of things I've read, wikipedia articles and plain speculation.
There is a very extensive and interesting article on wikipedia on low carb diets. A extract of what is written there:
^"The body of research underpinning low-carbohydrate diets has grown significantly in the decades of the 1990s and 2000s.Most of this research centers on the relationship between carbohydrate intake and blood sugar levels (i.e. blood glucose), as well as some related hormone levels. Some evidence suggests blood sugar levels in the human body should be maintained in a fairly narrow range to maintain good health. The two primary hormones that regulate blood sugar levels are insulin, which lowers blood sugar levels, and glucagon, which raises blood sugar levels. These are both produced in the pancreas: insulin from beta cells and glucagon from alpha cells.
In western diets (and many others), most meals are sufficiently high in nutritive carbohydrates to evoke insulin secretion. The primary control for this insulin secretion is glucose in the blood stream, typically from digested carbohydrate. Insulin also controls ketosis; in the non-ketotic state, the human body stores dietary fat in fat cells (i.e., adipose tissue) and preferentially uses glucose as cellular fuel. Diets low in nutritive carbohydrates introduce less glucose into the blood stream and thus evoke less insulin secretion, which leads to longer and more frequent episodes of ketosis. Some research suggests that this causes body fat to be eliminated from the body, although this theory remains controversial, insofar as it refers to excretion of lipids (i.e., fat and oil) and not to fat metabolism during ketosis."

So, the main idea it to reduce the amount of insulin secretion (that is the low carb part). This will induce a state of ketosis, where instead of using glucose, the body will use ketones to get its energy. The higher fat intake is necessary to have enough energy from the food and to ban the hunger from the diet. The body feels sufficiently nourished and does not lower the metabolic rate to accommodate for lower energy intake (i.e. starvation mode). Then you become an efficient "fat burning machine". I really recommend to read the wikipedia article on low fat diets. It outlines well the ongoing scientific debate about nutrition.
Another interesting wiki-article is about insulin release. These diets eventually aim for lowering the insulin release from the body. So it is most natural to want to know the insulin response to food. What is surprising from the article is the sometimes disproportionate insulin release to the carb content of some food, for example beef. But I think it would be very hard to know the insulin release of combined foods, like a soup. It anyways gives a good indication.

The insistence on the ban of trans fats is hardly surprising (what it is surprising is that they still manufacture it to give it to people) as those fats are really bad for health. The insistence on eating saturated fats is controversial.