The main conflict in the novel exists between Erik, the Phantom, and his pupil, Christine. It is from this where the other conflicts and subplots reveal themselves. Essentially, the conflict is whether or not Erik will let go of his love for Christine. He tutors her and trains her. He develops a love for her, only to find that she is in love with Raoul. This is where the conflict of the novel is present.
From this, the hiding in shadows, immersion into a life where appearances and reality differ, and one in which individuals must place a primacy on what they value become evident. The conflict in which the Phantom demands Christine's love is one in which he recognizes that he cannot stand in the path of true love. In sacrificing himself and always being reminded of what it means to nurse a broken heart, the Phantom provides resolution to this conflict. It is in the fundamental conflict between the Phantom's love and Christine's love where the novel takes place.
The central conflict in The Phantom of the Opera is between Erik, or the Phantom, and Christine, his pupil and love interest. The trouble is that the Phantom is in love with Christine, but Christine is in love with someone else -- the more age-appropriate and dashing Raoul. At least, that's how it seems on the surface.
There's another angle here, however, in which we can see the conflict as one between teacher and student, or between a man who wishes to objectify the woman and a woman who wants to be her own person. Erik feels entitled to Christine's love--he feels that he has created her by cultivating her talent and making her a star. Christine, for her part, is torn between respect (and fear) for her teacher and her desire to escape and be with Raoul.
Erik releases Christine in the end, and it is meant as a grand gesture of sacrifice--but all along he has been confused about who she really is and about the true nature of love.