Empathy is innate to humans when they are born. This is relevant because only sociopaths are unable to feel emotion for another living creatures. Sociopaths are chemically imbalanced individuals, and have and rare excusable lack of morals. Being that empathy consists of the ability to intellectually identify ones feelings, thoughts, and attitudes based on their perspective and personal experiences it is only true that it is a given trait as a new born baby.
People always get freaked out when their beloved child first lies to them - but really, they should be celebrating an amazing developmental milestone, the recognition that one's mind is separate from someone else's and they can't see in. I think that recognition comes before the development of what we most usually mean by empathy. That infant sense is actually quite narcissistic, and it takes quite a few years before the combination of knowing oneself separate and being able to imagine or feel how it is for someone else provides the possibility of the sort of empathy that leads to compassion. As shown by MRI studies show that certain areas of the brain are active when we perceive other people or animals in pain, and are the same areas as activated by our own pain, so it seems that the brain is designed for empathy.
The current view is that the capacity for empathy is innate as a latent function, but that and the behavior itself is learned as children grow, and indeed is continued to be learned through adulthood. People also link empathy to other factors such as self-esteem, although again I think it's a bit more complicated than that. For instance I think that healthy self-esteem allows people to deal better with empathy, not necessarily to experience it more in the first place and use it actively. Nancy Eisenberg, a psychologist at Arizona State University, agreed. “Children need a positive, caring relationship with their parents or caretakers,” she said in an interview, “if