I read/heard somewhere that all birds feed their babies insects, in order to get the lipids (fat) to fuel growth. I should also imagine there is more protein in insects than there is in fruit. (Basic biology: birds & other animals get their energy from food, classified into three categories--carbohydrates (sugars, both mono- and di-saccharides and starches, longer carbon chains), protein (amino acid chains, contain nitrogen), and lipids (long carbon chains not soluble in water). For food the unit of energy is the Calorie. One gram of carbohydrate or protein yields 4 Calories of energy while 1 gram of lipid yields 9 Calories. When lots of energy for fast growth or for migration is your goal, lipids are your choice.)
So it makes sense that fruit-eating birds (waxwings) would be seen chasing insects.
