You need all that stuff, so don't wreck your brain and body because you're afraid of consuming fat. Just try to make sure you're favoring eating more unsaturated fat in the form of plant oils, fish, and nuts than saturated fat -- though red meat does contain some unsaturated fat, so don't kill yourself if you can't resist that burger every once in a while.
A cautionary note
Even though these are the good types of fat, don't go bonkers as you chow down -- no matter what kind of fat you eat, it still provides nine calories per gram, which is more than double that of what carbs and protein will give you (both provide four calories per gram each). The good news is that eating fat will help you feel full faster, requiring less input than carbs or protein.
So thanks, fat. Thanks a lot! As long as you do it right, fat can help you shed weight, which is what you've dreamed about your entire life, right?
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