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.
There are several female pediatricians in my children's doctor's office - who all agree that after med school and residency and everything else - ped's was one of the best areas of medicine to practice and have the time to personally raise a family.
Most of the doctors keep very liveable hours (on call once a week and very few "emergency" calls unlike surgeons or ER doc's), have tons of flexibility (ie: leaving at 3pm to go to their own child's soccer game), and make enough money relatively quickly to afford vacation time.
Typically the reason of "loving children" is true for ped's - therefore they also wish to have their own.
The previous thoughts were quite accurate. I would say that the ability to help children across the world could be one major compelling factor in the desire to become a pediatric physician. To be able to offer medical care to children is compelling in its own right. Yet, to be able to take this gift to different nations or countries where health care for children is an after thought or might not be able to be easily afforded could be extremely convincing. Even in a larger sense, to be able to give care to children in any area of the world or in one's own locality where children might not be able to experience such care could be justification enough to want to enter the field. In a more globalized world and in a realm where strict borders are disappearing, the need to provide more care through pediatricians who are there is a very powerful one.
There could be many reasons why a person would want to become a pediatric doctor. Usually the reason that people choose the medical profession is because they have a calling to help people. In addition, for a person to choose pediatrics would mean that they would have to love working with children. There will always be new experiences and every day will bring something new. Medicine can be a very fulfilling career. I have personally known many physicians and I have not met one that has not been very passionate about their job.