Sometimes this phrase gets a bad rap, and maybe, at times, rightfully so when it is cliché or excusatory for unkind words and actions. But, interestingly, in Mere Christianity, none other than C.S. Lewis gives a defense/explanation of it. I find the way he slices it helpful.
[A]pparently 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.
C.S. Lewis, Mere Christianity, book 3, chapter 7, paragraph 6-7.
The Lord enjoins us to do good to all without exception, though the greater part, if estimated by their own merit, are most unworthy of it. But Scripture subjoins a most excellent reason, when it tells us that we are not to look to what men in themselves deserve, but to attend to the image of God, which exists in all, and to which we owe all honour and love. … Say that he is unworthy of your least exertion on his account; but the image of God, by which he is recommended to you, is worthy of yourself and all your exertions. … We are not to reflect on the wickedness of men, but look to the image of God in them, an image which, covering and obliterating their faults, should by its beauty and dignity allure us to love and embrace them.
John Calvin, Institutes of the Christian Religion, book III, chapter 7, section 6.
When you first read the words, “Love is not selfish” you may have immediately thought of 1 Corinthians 13, frequently called “the love chapter.” However, these words actually never appear there. Yet, I still believe this statement is very true. Even from Paul’s words one can see this principle: “Love does not envy or boast; it is not arrogant” (v.4) and “It does not insist on its own way” (v.5). Let us take a brief look at what I believe is a vital characteristic of true love.
Our culture has taken the word love and distorted it completely. I’m not taking just about the fact that it has made love synonymous with physical romance, but the fact that it has subtly made love into something selfish. What do I mean by this? Love has come to mean “strongly appreciating someone for loving you as much as you do.” We only “love” those who please us. We only “love” the actions and attributes of another that benefit us. We “love” them because we like being loved.