Because Michael, The Parrot Wizard, "follows" Bird Tricks, and both have recommended starving their birds in order to get compliance. They don't consider it starving, but when your bird looses weight (even if the bird was overweight and gets to a healthy weight and that weight is maintained), and feels like they are starving, the birds can revert to baby behaviors and result in stress.
There's other reasons as well, but that's just one of them.
Barbara Heidenreich goes over weight management, which Michael thinks is the same as food management, and it's not.
Weight Management in Animal Training: Pitfalls, Ethical Considerations and Alternative Options
Weight Management Revisited
Weight management is for falconers, and when used correctly, can keep birds at a higher weight than what is considered the average healthy weight while still maintaining desired behavior.
Michael on the other hand pretty much said to get your bird 10% *UNDER* what they should weigh and to keep them at that weight. Well, when a bird loses 10% of their body weight, it's usually best to take them to an avian vet... granted, Michael does say to get the bird's weight down 2% each week, so it would be over 5 weeks that the bird would lose 10% of their body weight... but when it comes down to it, it's food deprivation. Not healthy. Not physically, not mentally.