One of the hardest statements that Jesus ever made was his admonishment to love our enemies. To understand why this was so hard we have to remember the audience that Jesus was talking to. The Jews of Palestine at that point were an occupied people. Rome had been their overlords for decades and the dream of the Jewish people was for the promised Messiah to come and over-throw them.
So when Jesus tells his audience in the Sermon on the Mount that they are to love their enemies, pray for those who curse them, turn the other cheek and go the extra mile, he's not simply talking about loving and responding kindly to those who speak badly about us. What he is talking about here is a radical love that goes beyond loving those who love us; he's talking about loving people that seek our harm, that go against everything we as followers of Jesus might stand for.
In his book, The Sacredness of Questioning Everything, David Dark talks about perversion and not simply in the sexual manner that we mostly think about perversion in. He points out that anytime we reduce someone to a caricature or to a single dimension of who they are, we are perverting them, because we're not taking into account the whole person, created in the image of God. Whether that is a woman that we look at and think is "hot" or even someone we classify as a "terrorist," looking at a single aspect of someone and defining the person by that aspect is perversion. And the worst form of that perversion is deciding to hate someone based on that aspect.
And so, when Jesus calls us to "love our enemies," what he's calling us to do is to actively look beyond a person as an "enemy," and to see God in them, whether they do or not. Because it is only in love that a heart can be changed, and that is what Jesus came to do, to turn the hearts of people back to the God that created them.