I'd add that keeping protein low is important too.
I would agree with this too, because eating large amount of animal-protein and especially milk-protein activates mTOR, and activating mTOR inhibits fat-loss. Plus most animal-proteins are high in calories and premade-fat (which your body effortlessly deposits in the adipocytes).
I think to lose weight in a healthy way is one you need to reduce total calories intake and also keep dietary-fat and insulin levels low. Foods like vegetables, oats, barley, pasta, lentils and homemade vegetable-stews which are all very low insulinogenic-foods would be cover all bases.
It doesn't contain premade-fat (which is easily stored).
It doesn't activate mTOR like sugars, flours and animal-protein does.
It doesn't cause a spike in insulin.
And it is low in calorie-density.
Now if you need to gain weight or stimulate growth or repair... you do the opposite.
You increase your ingestion of premade-fat (saturated-fat preferably, due to its greater ability to be stored within the adipocytes and its ability to stimulate leptin better than unsaturated-fats).
You activate mTOR by eating more animal-protein like skim-milk, whey-isolate or egg-whites.
You purposely spike your insulin with highly insulinogenic-foods like flour, sugar, potatoes, bananas and beans.
And you increase your calorie-density and palatability by eating more sugar and fat.