LFHC stands for "high fat, low carbohydrate." This is a diet some follow, including proponents of the Paleolithic approach to eating. Recommendations that we were meant to derive energy from fat and not carbohydrates, but NOT omega-6 fats (found in nuts and oils) leaves a paltry few foods to choose from, mainly animal products. Considering the bacterial contamination and pesticide residue found in animal foods, loading up on beef, fish and chicken is not a good idea.
Also, fat is a stored energy source but it is also the place where toxins are stored, like the garage of the body, and by eating the fat of animals you are getting all their stored toxins along with that stored energy. Anyone who says that carbohydrates are not a preferred energy source and this is why the body burns them preferentially (which seems very counterintuitive to me) is implying that we should not eat fruits and many vegetables, which are predominately carbohydrates and also some of the most nutritious foods, or that we should not be eating as the primates do, who have the same digestive systems and following instincts gravitate to fruits and vegetables over meat. Moreover, numerous studies suggest an association b/w high fat diet and cancer, diabetes, and Alzheimer's. (see below)
Also, fat in itself is very low in most vitamins and minerals. Fat-laden foods are some of the most non-nutritious foods out there. No whole foods exist that are pure fat. Animal foods (fish, chx, etc) provide a large amount of fat, but also a great deal of protein, more protein than your body needs to replenish muscle and enzymes, so the rest is either burned for fuel/excreted. Is protein therefore also a preferred energy source (over carbs)? Because that is what a meat eater is getting when eating high-fat animal foods. You cannot eat a lot of fat without getting a lot of protein unless you drink oil or consume lbs of butter (both pure fat, and neither a whole food). Therefore, in endorsing a high fat diet you must be prepared to endorse a high protein diet, and the research linking high protein intake with kidney disease and osteoporosis, not to mention cancer, is pretty solid.
Or does a HFLC advocate mean that one should be deriving calories from pure fat found in coconut oil and other processed foods? Is pure fat what should be substituted for the carbs found in fruit and vegetables? This too seems pretty nonsensical.
Fat is oxidized in the body, which causes free radicals to form. Too much fat therefore contributes to aging. When it is cooked it can become carcinogenic. Fat has over twice the amount of calories found in carbohydrates, and is therefore much easier to eat to excess. Consider that 2 tbsp. of peanut butter has more calories than 2 whole bananas. Fat is also much easily stored when eaten to excess, since it is ready-made, and because fat sends signals to the stomach to slow emptying, it is not absorbed as fast and therefore not as readily available for energy as simple sugars are.
If you want to reduce consumption of sugar, eliminate grains, but emphasize sweet fruits which are almost without exception low glycemic foods. To decrease sugar even further, replace some sweet fruit with good fats such as olives, avocados and maybe some coconut butter. All are fruits themselves and nutritious while also having high fiber, a rarity as far as traditional fat sources are concerned.