Some recent advances in our understanding of the biology of perspective taking and empathy can help us understand practical challenges and dilemmas of certain children.
There are developmental changes for perspective-taking (as well as probably normal biological variations), of course. One popular theory is Selman's (very briefly summarized):
Undifferentiated: Age 3-6. Recognition that differences can exist, but confuse the two.
Social-Informational: Age 5-9. Different perspectives due to differences in availability of information.
Self-Reflective: Age 7-12. Viewing thoughts and feelings from another person's perspective.
Third-Party: Age 10-15. Step outside self and others and see how a situation may be viewed by a third party.
Societal: Age 14-adult. See how third party perspectives can be influenced by different societal values.
The interesting scientific piece is how important sensory-motor (kinesthetic) systems are for taking another person's point of view. In the figure below, when subjects put themselves into a video clip (first person perspective), the sensory-motor area of the brain was the distinguishing area from a third person (bystander) perspective. An extrapolation of this might be -the better your your own sensory-motor experience, the better your empathy or perspective taking from another person's point-of-view.
This does make sense. We organize our experiences by representations, and when it comes to making speculations from them, the better initial reception or perception, the better we might be able to imagine how it would be for others.
It also makes sense why kids with sensory processing or sensory integration disorders from a variety of causes are often misdiagnosed with Aspergers or autism spectrum disorders despite close attachment to immediate family members. Missing sensory cues makes perspective taking more difficult, and this can result in a delay of perspective-taking or empathy milestones. In fact, there is a long literature documenting the delay in perspective-taking abilities among the hearing- and visually-impaired.
BTW, some of you might look with a skeptical eye on the notion that perspective-taking is higher for teens than younger children. Adolescents often get accused of having more egotistical points of view. This is a whole other can of worms, but at least some people think that teens' points of view become hijacked by other distortions like the Imaginary Audience ("Everybody's watching me") or the Personal Fable ("I am invincible"). If it's not one thing, it's another...
Selman's Perspective Taking Theory
The Power of Simulation - Empathy, Social Neuroscience
Imitation, Perspective-Taking, and fMRI
fMRI of Attention to Somatosensory Stimulation
Adolescence: The Imaginary Audience And Personal Fable