If your diet has less than 1 teaspoon of soybean oil (linoleic and linolenic fatty acids) per day you could develop a fatty acid deficiency. Symptoms are red, irritated skin , infections and dehydration. Also, the liver processes food fat and may develop abnormalities if fatty acids are deficient.
Your body uses fat to synthesize hormones and regulate blood pressure as well. Dietary fat also carries fat soluble vitamins A, D, E and K which could also become deficient if fat is too restricted.
Diets of less than 25% fat tend to reduce feeling satisfied after a meal. Bulimics tend to binge on carbohydrates when fat falls below 20%. The current recommendations are 25 to 30% calories from fat.
On the same website, there is a "Healthy Body Calculator". Here are the results for me:
If I want to lose 2 pounds per week, I should eat a 1200 calorie diet which would be 360 calories from fat, a total of 40g of fat with 13g of that saturated fat. To lose one pound per week, total calories should be 1,760, with 530 calories from fat (59g of fat with saturated fat 19g).