Interesting archaic theory, as me and my wife just lost 40lbs each by eating a ton of fat and protein, haha. If you want to lose weight, stay away from sugar, for example carbs
High fat high protein (with low carbs) can definitely be successful, as long as you’re mindful of your approach and manage net calorie intake. But for lots of people it is easier to just eat what they do, but make minor tweaks to reduce the amount of fat as a way of reducing calories while still being satisfied by what they’re eating. Different ways for different people.
Weight gain/loss depends on calories, so you can eat anything to either gain or lose weight as long as it's the proper quantity (although if you want to gain muscle then you also need enough proteins).