For comparison purposes a marathon is a pound of fat
spent in exercise, and you have to go through an
extensive and extended training program to get your
body to do that.

"Calorie is a calorie is a calorie" is false, but calories
work as an approximation.  "Calories in equals calories
out" is also false with any notion that calories out is fixed
(see my comment that a marathon is a pound), but it also
works as an approximation.  Do the calorie arithmatic.

A pound of stored fat is 3500-4000 calories.  To lose a
pound a week (this is fast no matter there hasn't been
dieter in history who likes calling a pound a week fast)
is a 500 calorie reduction below the point that starts
loss.  To lose 2 pounds a week is a 1000 calorie reduction.
Considering that human metabolism ranges from just
under 1000 calories per day among starving concentration
camp victims to over 5000 calories per day among olympic
class athletes, the maximum safe loss rate for fat is about
1000 calories per day.  Imagining that the maximum safe
loss rate is in any way sustainable is like imagining that
a competive sprint pace can be maintained for an entire
marathon.

If anything more than 2 pounds is lost in any one week,
something other than fat was lost.  Who among us wants
to lose lean muscle or bone mass?  I get that some folks
confuse water weight and fat weight so they want to lose
water, but water isn't fat and effort spent on losing water
is generally effort lost to losing fat.  There are some good
reasons for wanting to lose water, but water loss is a lot
more limited in total amount and in general usefullness.

Conclusion - There are realities when it comes to loss rates.
Places that cite faster rates can be written off as nonsense
simply by glancing at the numbers.  Nearly everyone
*wants* loss rates faster than possible or healthy, so sales
programs make up claims.