Theoretically not possible. Every cell membrane in your body is enclosed in a lipid layer cell membrane. Every nerve in your body depends on fatty insulation to be able to fire without interference. Every hormone in your body is fat based. That doesn't even begin to deal with the lubricants in your joints, lubricants needed between muscles, skin, organs so you don't turn into a solid, unable to move block (like a sufferer of scleroderma - ouch!).
Have fun in your argument! (O'course, your bro' may be like, don't confuse me with facts, man, my mind is made up!)