The narcissist is in love with himself, but he doesn’t love himself. That is because, rather paradoxically, while he is in love with himself he is estranged from his actual self. He is in love with his own projection, quite like the youthful (and, therefore, necessarily immature) love at first sight in which each lover projects their needs and desires onto the other, and therefore fails to see the other for who he actually is.
But where does that projection come from, then? It comes from the expectations of others: the narcissist sees, admires, and is in love with himself through the eyes of the others. The needs and desires which he projects on his own beloved image reflect his perception of the needs and desires of the others, and he subsequently strives towards becoming—or, rather, morphing into—that projection. On his way towards becoming the externally derived—and, thus, externally imposed—image, and of becoming himself convinced he actually embodies it, he loses touch with his actual self. The narcissist is in love with himself but does not love himself, because he is in love with himself through the external eyes of the others rather than the internal eyes of his own soul. In essence, he fails to see himself for who he really is (because the externally-derived projections of his self-estrangement stand in the way).
Bust also furthermore, being in love with someone—and therefore being in love with the projections of my own needs and desires— rather than loving him, means that I lack that someone and I need him in order to feel whole. On top of it not being a relationship with the actual person—and therefore not a “true relationship” in that sense—it is a relationship of need, it is underlined by the dynamics of addiction. The alternating highs and lows characteristic of being in love appear in narcissism as the unrealistically high self-esteem (the “I am perfect and people must worship me!”) and the profound insecurity it aims to defend the subject from (and from which it stems).
Therefore, while it first appears and serves as a defense mechanism, and while it has the appearance of love of the subject towards himself, narcissism is ultimately unable to satisfy his actual needs for self-connection just as much as it fails to satisfy his needs for connection with others.