I think that there are two main motivations for people wanting to be pediatricians. I think the first would be a love of practicing medicine. That should be inherent with every doctor. I personally would not a want a doctor that hates their job. A pediatrician might like practicing medicine because they find the human body fascinating. They love knowing how total body health works, and being a doctor allows them to help people get better. It's possible that a pediatrician enjoys the challenge and mystery of figuring out what is wrong with a patient. An adult doctor can ask a patient to describe how something feels. But a lot of the time, a child can't talk yet, or that child isn't able to effectively communicate what his/her ailment feels like. The pediatrician has a set of challenges that other medical practitioners don't deal with. That appeals to some people.
Beyond the few reasons that are already listed, I think a person would desire to be a pediatrician because they like kids. I can't imagine somebody that doesn't like kids wanting to be a pediatrician. That would be like finding a 3rd grade teacher who hates kids. Nobody goes into early age education if they don't like kids. I would assume it's the same with pediatricians. They like medicine, and they like kids.