A former student of mine just became certified as a pediatric doctor, so I texted her and asked her. Her response was immediate. She said "I love kids". When dealing with young patients, who are often afraid of doctors, hospitals, shots, pain, etc., you have to have a rapport and connection to them - they have to feel that you care. So if you don't love kids, I think it would be very hard to be a pediatrician.
I would think another reason is that, when giving medical care and treatment to kids, you are helping an entire family. Their world comes apart (especially the mother's, right?) when their child is hurt or sick, and a pediatrician can restore that world in some cases. As opposed to a geriatric doctor who deals with the elderly. It's a tragedy to lose one's parents in their old age, but we all expect it and it is inevitable. Anyone who loses a child would tell you it's an extra level of tragedy, because so much life was yet to be lived. A pediatrician can help in some of those cases, more so than in other medical professions perhaps. Lastly, a pediatrician works with preventive medicine - the nutrition and health of children is very important for the length and quality of their life later on, and a pediatrician has an immense amount of potential to affect that.