What diseases are caused by the deficiency of fats?

Weight loss: Weight loss, because fats have more calories/gram than any other food. There are some fat soluble vitamins like d that you might become deficient in, but it is very unlikely since you can't totally eliminate the fat from your diet no matter how hard you try -- and by the way, why are you doing it in the first place? Excess carbohydrate/protein (other two options) is not good either.