I tried googling, but the results aren't very useful with regard to the exact mechanism how thyroid problems cause weight gain.
Edit: From more reading I now believe that it's still a diet problem, but the thyroid issues seem to make it harder to eat less.
But I don't disagree that the thyroid issue makes diet harder, for reasons like increased hunger, less energy, etc(?)
Aaaaaand all your credibility just went out the window.
As someone else has pointed out, suffering from the same problems as the author has, doesn't make it impossible to lose weight, it makes it more difficult. If you provide your body with less energy than it uses, you're going to lose weight. Simple.
She says she's eating healthily, but is she actually?
Weight loss with thyroid issues (and, especially, with other complicating metabolic issues which often occur alongside thyroid issues) is not a simple thing.
People with metabolic issues do need diet/exercise balance to lose weight, but finding the right diet component that allows weight loss while maintaining health and the ability to function can require considerable expert assistance that wouldn't be necessary for a person without those issues.
"Maintain a calorie deficit" is easy to say, but can be very hard to do in a way which actually works.