I don't think anyone is born to hate.
I believe people learn to hate by the direct effect of the environment.
I want to know where exactly inside one's brain this hatred emerges and affects a person?
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From fMRI study, "Neural Correlates of Hate"
Viewing a hated face resulted in increased activity in the medial frontal gyrus, right putamen, bilaterally in premotor cortex, in the frontal pole and bilaterally in the medial insula. We also found three areas where activation correlated linearly with the declared level of hatred, the right insula, right premotor cortex and the right fronto-medial gyrus. One area of deactivation was found in the right superior frontal gyrus. The study thus shows that there is a unique pattern of activity in the brain in the context of hate. Though distinct from the pattern of activity that correlates with romantic love, this pattern nevertheless shares two areas with the latter, namely the putamen and the insula.
This is only a study in which hated faces were seen, so really it measures more than merely were hatred "is born", or it might not even catch that at all. It's not too clear how one could find that out.
Another paper has it more concisely as
the so-called ‘hate circuit' involving the superior frontal gyrus, insula and putamen
What's interesting in this latter paper is that this circuit was apparently "uncoupled" by depression.
Although it's veering off-topic, the authors of the latter paper have offered a less techincal interpretatoin of their finding in the mass media
"We were a bit shocked when we first saw these results," says lead researcher Jianfeng Feng, a professor of computer science at the University of Warwick who specializes in biology. Feelings of self-hatred are a common feature of depression, he explains, so one would expect those feelings to also be more intense when directed toward other people.
Instead, it's as if the brains of depressed people hate incorrectly. The brain disruptions the researchers observed could be a sign that people with depression have an impaired ability to cope with -- and learn from -- social situations in which they feel hate, Feng says. This may explain why they often turn emotions such as hatred and anger inward, instead of handling them in more constructive ways, he adds.
The thing to keep in mind that the "hate circuit" was labelled so after a narrow task (viewing hated images), which might not cover all the ways humans can hate. If the studies on love (which are more numerous) are a good analogy, "different types of love involve distinct cerebral networks, including those for higher cognitive functions such as social cognition and bodily self-representation". Although surely interesting, this line of research (on hate) is pretty much in its infancy (in my opinion).
Also, one cannot be certain a brain area is necessary for a certain function (say hate) just from brain imaging. One needs to "mess" with the brain area in question, which is usually unethical, except in rare cases, e.g. epilepsy patients who have had electrodes implanted. (I suggest you watch Kanwisher TED talk on this for more explanations.) In the case of the "hate circuit" no such evidence has been found yet, and history of neuroscience shows that it can take a really long time to have a confirmation like that for any association found by immaging.