I don't hear or see anybody saying that you shouldn't eat fat, just that a high fat diet may not be the best thing for all people. I have some students with significant seizure disorder who thrive on the ketogenic diet which is a very high, healthy fat diet: I'm jealous of the amount of shrimp these kids get to eat! I love shrimp!
Same for my diabetic students: they are on strict low-carb diets.
However, we also have students with heart conditions who can't have high-fat or fat anything.