I tell this to myself and anyone who wants to listen so I believe it but it bothers me that this is just the current "fact". A while ago, the opposite was "true", and who knows what we will all be thinking in the future? That, I think, is the most depressing thing about nutrition advice.
(The idea that complex carbs are problematic is somewhat newer, but sugar's been held to be a concern for a long time -- that's why its broken out separately from general carb totals on nutrition labels.)
In a nutshell: long-term nutritional studies are hard and expensive, scientists of the era jumped to some conclusions without the gold-standard double-blind experiments that are expected of scientists today, and once the mantra of low-fat (and high-carb) diet being good for you was accepted by a government-run National Institutes of Health, chances of grant money going towards scientific study proving otherwise are virtually nil (did I mention those studies are hard and expensive?)
I myself am doing keto with Ketochow (a Keto-esq Soylent mixture made by a gentleman out of Utag), and lose 3-5 lbs a week on it (yet it tastes like delicious pancake batter) while doing minimal exercise.
It's obviously a combination of eating less and losing water weight. Your body can maintain about 1 lb of glycogen and 3 lb of water associated with that glycogen. Not eating carbs will likely lead to a big decrease in this weight. Also the fat itself is stored in 1:1 ratio with water. So your 3-5 lbs per week is likely either a 1 or 2 time thing where you progressively lose all your glycogen. Together with a moderate calorie restriction you end up losing some fat and an equivalent amount of water.
There's plenty of people losing 15 - 20 lbs per month.
Not only are my macros significantly skewed towards fats now, I am indeed consuming less calories (only 1000 cal/day of Ketochow) while still feeling satiated. My TDEE is ~2200 cal/day.
The actual range for the weekly calorie deficit is more like 1800 (3 pounds, 100% muscle @ 600 Cal/pound) to 17,500 (5 pounds, 100% fat @ 3,500 Cal/pound)
And if you are doing losing weight through calorie deficit with a basically sedentary lifestyle, the percentage of weight loss through fat is probably going to be no higher, and possibly substantially lower, than your starting body fat percentage. The key reason for working out while losing weight is maintaining muscle mass.
Less protein is converted to glucose than carbs but you can still eat too much protein and kick yourself out of ketosis. Fat converts to glucose at the lowest amount of the 3 macros.
It's hard for people to understand dietary fat != body fat because they've been basically "fed" bullshit their entire lives by advertisers and our own government guidelines. So many people think "low fat" is healthy but all it usually means is "we took the fat out and gave you more sugar".
I'm a bug fan of keto but I wouldn't recommend every one do it. I would recommend everyone cut their carb intake in at least half, unless you are some kind of endurance athlete but then you probably know enough about your body to know what to eat. We eat way too many processed foods which means way too many carbs and not enough of them are fiber. Many people probably don't even realize how many carbs they eat in a day.