Some back story first: The Phantom grew from a child who was never loved because of facial disfigurement. He was mistreated from childhood and grew to be a very talented, but very twisted man. He victimized himself and blamed his choices in life on his misfortunes. Christine, herself, points out that his dark fate is not simply a result of his outward appearance but the condition of his soul (implying that his choices led to where he was at that point: a seductive liar and murderer.)
So near the end, The Phantom is threatening to kill Christine's fiance if she did not choose to marry him. The situation seems hopeless and here's what intrigued me:
Christine and her fiance, Raoul try a few different methods of arguing and reasoning with the Phantom as he is on the verge of murdering Raoul.
This has only a small effect on the Phantom and he continues to threaten.
Next Christine tries a guilt-trip. Acting hurt she says that she trusted him and he deceived her.
This also has little effect. The Phantom says she is trying his patience.
Finally, something breaks. This scene makes me think of an illustration I have thought of when dealing with people. If people feel threatened or want to pick a fight or control things it's like tug of war. If you pull on the other end of the rope then it is a full-blown battle, but if you let the rope loose a bit, the fight is over and the other person feels less threatened and becomes more trusting. Peace is restored. I don't know if this is what was going through Christine's mind but she suddenly changes her tune. Looking on him with compassion she comes and speaks to him and touches him like no one ever has. She says, "pitiful creature of darkness, what kind of life have you known? God give me courage to show you, you are not alone!"
With that, the Phantom is overcome. He sees how her actions came out of kindness and this gives him a measure of honor within himself. He suddenly frees them to leave.
Christine and Raoul are safe, the Phantom is overcome and does find love in his heart for Christine especially now that he saw her selflessness in showing him - a monster - true love.
You may say Christine did that to seduce him into letting them go.
You may say Christine really loved him.
You may wish that Christine would be with him.
Maybe it was desperation that she chose to kiss him.
Here is what I saw: Christine did not love him as a partner but she showed him true love by putting his need for someone to care before her own needs. She chose a new way, a way of compassion and love to change a heart - even by a small measure.
I just think it was so profound, so beautiful. I am glad she went with Raoul, he was what she needed. Raoul was the sensible, realistic choice. The Phantom never forgets her kindness.