I think the Christian would answer that one can love thy enemy and control thy anger when there is a complete submission to the will of Jesus. Part of Jesus' teachings was that all human beings are children of God. If one recognizes this, then there are no enemies. Those who do wrong should be forgiven for transgressions. Detest the sin, not the individual. The thinking here is if Jesus was able to make the ultimate sacrifice for the sins of humanity, then we as human beings and his descendants can sacrifice our hatred and anger in his example. Clinging to hate precludes full recognition of his teachings in our own lives. I think that the Christian would suggest that if Christ represented a pure and universal love for humanity, how can holding on to anger and spite enable his example to enter our lives? It is a tough ethical standard, but this is the sacrifice that one makes in being a devotee of Jesus. It has been said that Jesus gave the world a "moral conscience." Part of this is being able to submit our own anger and wrath to him, allowing his "better angel" of our nature to emanate through our being.
In many senses, the Christian would argue that anger is a reflection of this world. It is a reflection of the world of man. It is temporal. Jesus' teachings make the point that there is a difference between the contingent world of here and now and the true world of the divine. Jesus' teachings stress that the lessons learned in this life to better prepare us to accept the world that follows this one. Letting temporal issues go in way of something larger is integral to this lesson of Christ. If one reflects about what was deemed worthy of "anger" ten years ago, there might be a good chance that it is not the same way today. Part of this reflects the temporal nature of anger. We are angry today, right now at this instant. Yet, Jesus' love and his lessons are transcendent. They are taught to be the ultimate reality, devoid of temporality. It is for this reason that Jesus says we are able to hand our anger over, surrendering it because this moment is not all of our moments. It is a moment in time. It is of this world. When we accept this, the teachings of Christ says that we are able to recognize that which is real and universal. In recognition of this condition, turning the other cheek is not difficult at all. Put in another way, anger can be seen as an attachment. It is an attachment of this world and of this life. If we seek happiness, then we must find a way to not be attached to what is in this life. Severing the bonds we have to anger is a part of this process. Jesus' teachings stress that in order to prepare the way for what is real and universal, there must be a distinction made between this temporal being and the more transcendent one. Anger is a part of this condition, something that can be shed in following his example of universal love for thy brother. Turning the cheek can be done in this light.
It is important to stress that much of this is not intrinsic to only Christianity. The same ideas of surrendering to the will of the divine can be seen in Hinduism in being able to place the problems of this life at the divine lotus feet of Lord Krishna, Lord Shiva, Durga Devi, or Lord Ganesh. The stress on surrendering attachment in order to find true happiness is a central tenet of Buddhism. This only enhances the universality of such teachings.