It is easy to like people who like us, and respect people who respect us.  It is the natural way society works.  It is also natural to hate those who hate us and curse those who are against us.  But Jesus was not like that!  Paul was teaching Christians in the high profile, high pressure, city of Rome to live a radically new life - like that of Jesus (Romans 12:1).  In that way, they would demonstrate the in-grafted nature of Jesus Christ as they interacted with the people they lived and worked among.  The context of the first half of Romans 12 was how to live with believers, and now he is extending this teaching to living with hostile unbelievers (Romans 12:20).

Instead of cursing those who make their life difficult, to retaliate in anger or revenge, people who follow Jesus should bless their persecutors (Acts 7:57-60).  This is a supernatural response, only made possible by the Holy Spirit's work in the heart of the child of God.  That was how Jesus responded, and He practised what He preached (Matthew 5:44, Luke 6:28), even when He was being falsely accused.  On the cross He prayed for His persecutors and even the execution centurion was amazed at how Jesus behaved, and said, "Surely He was the Son of God" (Matthew 27:54).

Disciples of Jesus stand out from the crowd because of two reactions: they love their fellow believers even though they may be of a different race or social class (Galatians 3:28), and because they love their enemies (1 Corinthians 4:12-13). The supernatural response to hostility is love, because God has set His love into our hearts by the Holy Spirit (Romans 5:5); and compassion, because they are like sheep without a shepherd (Mark 6:34).  God’s great desire is not that they should be destroyed, but that wicked people may be saved if they receive Jesus (2 Peter 3:9).  

The Lord has given us the motivation and the power: we just need to put it into practice.  The first step is to pray for those you would naturally hate; they will not be able to change unless God changes them.  Pray as Jesus did, "Father, forgive them, for they do not know what they are doing" (Luke 23:34).  That is the challenge, first to pray for those who hate you and then choose to ask God to bless them.