There are two issues with that criticism of a low-carb diet:
1) Flour and whole grains don't have the same effect, but whole grains are much scarcer in the modern food environment.
Joe Rogan joked, "if your trainer is telling you to eat bread, find a different trainer. That sh*t is terrible for you."
To bake wheat into bread, the wheat has to be pulverized into flour. Bread made out of truly whole grain would be all but inedible. What modern industrial bakers call "whole wheat bread" is just white bread with a little bit of the pulverized bran mixed in. Often it's not even that, it's just white bread with caramel coloring.
Flour has a terrible effect on the body. The flour becomes simple sugar very quickly in the body, causing a dramatic rise in blood sugar, with all of its downstream problems. So if someone is essentially saying "you can't cut out carbs entirely", they might be right, but they don't, or shouldn't mean you should eat flour. Good carbs are from green leafy vegetables, and depending on carb-tolerance fruit, beans, and whole grains. The problem is that, with whole grains in particular, these foods are much scarcer in the modern food environment. When was the last time you saw farro on the menu at a restaurant?
2) People have differing levels of carb-tolerance and blood sugar issues.
As I said above, flour raises blood sugar. It's not only flour though. A cup of brown rice still has a significant amount of sugar bound together in its carbohydrate content. Parroting Virta Health's youtube channel here: someone who is diabetic, or pre-diabetic, probably (on an individual basis) shouldn't be eating even these complex carbs.
Even if you don't have an issue with being overfat, have high blood sugar, abnormal lipids, or high blood pressure, one can still make the argument that, at the very least, it's not a good idea to eat a lot of processed flour as this may, over time, lead to those very conditions.
Conclusion
The person giving this advice might not have the same carb-tolerance as you do. They might be naturally lean, have normal blood sugar....etc. For them, eating carbohydrates, maybe even eating processed flour, doesn't seem like a problem. For me though, with a current BMI of 42, a fasting blood sugar of 105, and high LDL cholesterol, it's a very different story.
Often, if the person giving this advice means "flour" when they argue to add carbohydrates to the diet, there is a pretty cogent argument that they are just plain wrong. If they are one of the truly exceptional people that eats a lot of actual whole grain, and that's what they mean when they argue for adding carbohydrates, they might be more correct, but it depends on your level of carb-tolerance and your current health situation.
I eat a low-carb diet, but I also eat a lot of green leafy vegetables that grow above ground. I don't currently eat beans or whole grains. On this diet, I have had good success with weight loss, how I feel day-to-day, and motivation to make other health changes like adding more exercise. I might experiment with more liberal carbs in my diet periodically as a way to stay motivated to largely eat low-carb, and I may liberalize my diet as my weight goes down. For now though, I eat low-carb (+ veggies), and I especially don't eat much, if any flour.
