C.S. Lewis, as usual, says it much better than I can.
An excerpt from Mere Christianity:
I believe the one I have to talk of today is even more unpopular: the Christian rule, “Thou shalt love thy neighbour as thyself.” Because in Christian morals “thy neighbour” includes “thy enemy,” and so we come up against this terrible duty of forgiving our enemies.
… we might try to understand exactly what loving your neighbour as yourself means. I have to love him as I love myself. Well, how exactly do I love myself?
Now that I come to think of it, I have not exactly got a feeling of fondness or affection for myself, and I do not even always enjoy my own society. So apparently “Love your neighbour” does not mean “feel fond of him” or “find him attractive.” I ought to have seen that before, because, of course, you cannot feel fond of a person by trying. Do I think well of myself, think myself a nice chap? Well, I am afraid I sometimes do (and those are, no doubt, my worst moments) but that is not why I love myself. In fact it, is the other way round: my self-love makes me think myself nice, but thinking myself nice is not why I love myself. So loving my enemies does not apparently mean thinking them nice either. That is an enormous relief. For a good many people imagine that forgiving your enemies means making out that they are really not such bad fellows after all, when it is quite plain that they are. Go a step further. In my most clear-sighted moments not only do I not think myself a nice man, but I know that I am a very nasty one. I can look at some of the things I have done with horror and loathing. So apparently I am allowed to loathe and hate some of the things my enemies do. Now that I come to think of it, I remember Christian teachers telling me long ago that I must hate a bad man’s actions, but not hate the bad man: or, as they would say, hate the sin but not the sinner.
For a long time I used to think this a silly, straw-splitting distinction: how could you hate what a man did and not hate the man? But years later it occurred to me that there was one man to whom I had been doing this all my life-namely myself. However much I might dislike my own cowardice or conceit or greed, I went on loving myself. There had never been the slightest difficulty about it. In fact the very reason why I hated the things was that I loved the man. Just because I loved myself, I was sorry to find that I was the sort of man who did those things. Consequently, Christianity does not want us to reduce by one atom the hatred we feel for cruelty and treachery. We ought to hate them. Not one word of what we have said about them needs to be unsaid. But it does want us to hate them in the same way in which we hate things in ourselves: being sorry that the man should have done such things, and hoping, if it is anyway possible, that somehow, sometime, somewhere, he can be cured and made human again.
I admit that this means loving people who have nothing lovable about them. But then, has oneself anything lovable about it? You love it simply because it is yourself, God intends us to love all selves in the same way and for the same reason: but He has given us the sum already worked out on our own case to show us how it works. We have then to go on and apply the rule to all the other selves. Perhaps it makes it easier if we remember that that is how He loves us. Not for any nice, attractive qualities we think we have, but just because we are the things called selves. For really there is nothing else in us to love: creatures like us who actually find hatred such a pleasure that to give it up is like giving up beer or tobacco. …