When you think about, if the moon, the first waterbender, is a waterbender, shouldn't Yue be too?
Disclaimer: I don't own Avatar, and never will. Whoopee.
But, I do own this plotline.
The Spark of Rebellion
The little girl cried out as she tripped and cut her knee on a jagged piece of ice. But there was no one nearby to help her. As she held her knee and cried, her hands started glowing unnaturally. Blinking in surprise, she took her hands off of her knee and gasped. It was completely healed.
Yue remembered the first time she learned she could waterbend. It had surprised her four-year-old self to be able to heal almost any hurt. But at almost 14, she wondered if she could do other waterbending too. She had watched Master Pakku and his students learn to do 'The Single Water Whip' and other techniques. One day, she went up to Master Pakku and asked him if he would teach her. He just stared at her, then laughed quietly, shaking his head. "Princess, only boys get to learn waterbending." She was appalled. But she just turned away, being the obedient princess she was. As she walked away, a spark of rebellion sprang up from inside her, and she almost turned around. But Yue just smiled to herself and kept walking. She had a plan.
The next day, Yue found a hiding place that was quite roomy, and had a perfect view of the waterbending classes. For two and a half hours she watched them and copied their moves. She was waterbending! But she was messy, and uncovered her hiding spot. Yue had never seen her father so angry. He locked her in her room and told her never to waterbend again, except for healing. The spark of rebellion was diminished.
Two years later, the spark of rebellion sprang up again, when the Avatar and his friends came to the North Pole. The Avatar's friend Sokka was so handsome and so brave, it broke her heart that she was to marry that jerk, Han. Yue was so close to defying her father and marrying Sokka, but the obedient and dutiful princess took over. But Yue avoided Han in another way. She left the North Pole, and left the world of mortals. She became the moon spirit, for the moon had touched her, giving her her white hair, her waterbending, and probably that little spark of rebellion.
This is kind of a sad story. But I like it.