So your argument is that fat doesn't actually contain any calories?
The big difference is that when your body is loaded with carbs, it's a sugar-burning machine rather than a fat-burning one. And excessive carbs are converted to fat and stored away. As one continues on a high carb diet, the stored fat isn't needed for energy, therefore isn't used up. When a person limits the amount of carbs eaten, the sugar in the system is used up and the body is forced to start burning the stored fat for energy. Weight loss starts to happen.
I'm not a very active person at this point (although shedding 37 pounds has allowed me to become more active than I was when I started Atkins) so I don't eat nearly as much food as I used to before Atkins. The fat I take in helps give me a full feeling and I'm much more satisfied for a much longer period of time. No more cravings, no more sugar crashes, with higher energy levels that last much longer, and a LOT of ailments I believe was due to excessive carbs have or are disappearing. The type of fat in my diet is varied, from hamburgers to fish oil to olive oil for eggs. I still get two to three cups of veggies a day, eliminating the veggies with starches like corn, carrots, and potatoes. For some reason, salmon is great for me!
I also believe Atkins is much healthier because I'm not eating a ton of processed foods as I was on Weight Watchers. Because Atkins is pretty restrictive, Weight Watchers appealed to me (after I had started Atkins) because of the variety of foods I could eat. The problem was so much of the low or no fat foods are very processed, I was consuming a huge amount of carbs, I was continually hungry, and in no time my symptoms flared up. And the weight loss almost came to a halt. All while I was within my "points." I switched back to Atkins and within the week my health improved considerably not to mention I was losing weight nicely again.
I am careful with this diet by drinking alot of water, taking vitamins and minerals Atkins recommends, and constantly monitoring my health and the foods I'm eating. My prime motivation is to gain my health back and avoid the diseases that come with obesity, the weigh loss is a bonus. My own doctor also encouraged me to continue Atkins which is just icing on the cake.