Empathy is a good skill to evolve, allows a more balanced opinion, both in terms of rational thinking and inner peace. However, the relationship between empathy and conflict resolution isn’t straightforward as it seems:

The width of this empathy gap did not correlate with a person’s empathy rating on personality assessments; it was not wider in less empathetic people or narrower in more empathetic people.
— J. Interlandi (2015) The Brain Empathy Gap

This is incredibly counter intuitive: we would expect that more developed empathy would correlate with a better understanding of the other, thus less conflict. This isn’t the case.

A group of researchers at MIT is looking into the correlation of empathy and inter-group conflicts.

We find that self-categorization and competition not only dampen empathy, but also engender counter-empathic responding toward out-group members.
— M. Cikara, E. Bruneau, J.J. van Bavel, R. Saxe (2014) Their pain gives us pleasure

In other words, the stronger is the sentiment toward the group you belong and the stronger is the perceived competition between you and the people from the other group, the easier it is for our brain to override empathy.

“The more an individual’s team affiliation resonated for them, the less empathy they were likely to express for members of the rival team,” he says. “Even in this contrived setting, something as inconsequential as a computer game was enough to generate a measurable gap.”
— E. Bruneau via J. Interlandi (2015) The Brain Empathy Gap

This clearly isn’t an easy problem to solve, however the research above shows us how even the simplest separation in groups – as arbitrary as a division in teams to play a game – is able to elicit the dampening for the sufferings of the other team.

There’s some hope however:

He reasoned that something somewhere in their lives had overridden their implicit biases and moved them to behave with greater empathy toward the minority group. He wanted to know what that something was. “If we could figure out how it happens,” he said, “maybe we could harness it somehow.”
— J. Interlandi (2015) The Brain Empathy Gap

So at least, we know one of the factors to pay attention to in trying to address these problems.

Thanks to Daniel Szuc for the link.