Why do i need a calorie deficit to lose 20 pounds if the calories needed to maintain my weight is the same whether i weigh 115 or 102 pounds?

Weight loss: Your caloric requirement is just a guess- the amount required for a 115 and 102 lb person is different, but not by a whole lot. The caloric deficit you will need to maintain to lose 20 lbs is way more than the piddly difference between the metabolic requirement. To lose 20 lbs in 6 months you will need a deficit of about 400 cal/day every day.