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There may be several reasons. First, our bodies need fat to function and tend to store more calories when not getting adequate fat (20 percent to 30 percent of calories).
Next, low fat and fat free versions of foods often contain more calories than their full-fat versions. The labels usually reveal more salt and sugar to improve the taste.
Last, it would be difficult to get adequate protein when restricting all fats, so I encourage you to reconsider a balanced diet.