When I read "2kg/week", I almost jumped. That is a big number! Google tells me that 7,700 calories must be cut from your "normal diet" to lose 1kg of body weight. It would be an incredible feat of willpower to consistently cut 15,000+ calories per week from your "normal diet"!

It's not easy but certainly possible. For a reasonably tall male (higher calorie burn), being active (>15k steps a day) while eating around 1500 calories a day will lead to a deficit of up to 15,000 calories a week. Eating 1,500 calories per day is restricting but not starving, and burning 3,500 calories per day is a very active lifestyle but not some extreme sports or so.

But as others have noted, it often doesn't seem to be sustainable as your body will react to that kind of calorie deficit.

Cutting down to just essential amino acids and other essential nutrients like some select fatty acids, cushions, and minerals, isn't that hard if you can avoid carbs from getting advertised to you. Even a non-optimized protein source like eggs easily offers ~500kcal/day at sufficient protein levels, and sustained keto doesn't really include hunger feelings. It's not particularly healthy, but if the only way to keep up a significant caloric deficit is to see the rapid results of this kind of diet, it should still be healthier than morbid obesity.

That 7700 per 1kg figure is for Fat. However what you burn through first are Glycogen stores [1] which store about as half as much energy in the same weight as a more readily available form.

https://en.wikipedia.org/wiki/Glycogen

Exactly, and I feel like that's subconsiously the point of setting a goal like that. It's unattainable, so by conflating it with weight loss in general, of course weight loss isn't possible, which is a sentiment you will see repeated quite frequently in any online weight loss discussion.

My max. sustainable weight loss rate seems to be about half a kilo a week. Any more and I start yoyo-ing.