To me and many other Zutarians, Mai represents the life Zuko used to have, the life he used to be happy with. She is, in a way, a symbol of the Fire Nation, the Nation he wanted to get away from. He knows, however, that even if she tried, she wouldnt ever understand him. To her credit, she has tried. But Zuko would pour his heart out to her; tell her about all the struggles he went through. And what would she do? Thats right; she would arrange a meeting between her tongue and his tonsils. You cant just kiss your worries away. And finally, in Nightmares and Daydreams, Zuko had had enough. He had put up with that for long enough. And when Mai turned his face toward hers, he did not reciprocate. He turned away. And it is blaringly obvious that this was the episode in which Zuko realized that this was not his place. It was not where he was supposed to be. He had tried pretending he was happy here, in this relationship, and with the people around him as well. But he knew it had to stop. His goal, starting right about the time of the war meeting, was to bring peace to a war-torn world. Mai, really, couldnt care less about it.
Katara, in the mean time, is a very sympathetic person. In *Sozins Comet*, Zuko confided in Katara when he was about to see his uncle again. She didnt hug him or kiss him or give him a neck rub. She sympathized with him and offered him wise words of comfortnot to mother him, but to calm him. When Mai decided to make out with Zuko towards the end of The Beach, that did not comfort him; it merely sustained him.