To begin with, I've learned that having a teacher who is motivated is one of the key aspects to a students motivation. In the 10 years that I was dancing, I had three different teachers, but the one I learned the most from was the one that was there with me showing me the steps. I had teachers that would simply sit down and tell me what to do, but I didn't learn nearly as much from them because I saw that they weren't motivated to teach. And as result, I wasn't as motivated to dance.
Flamenco also taught me a lot about working with other people. Many think that there's no competition involved in dancing, but I think you would be surprised to see how competitive the dance world really is. I'll never forget how all of the girls used to fight to be in the middle, because she who was in the middle was considered "the best". The worst was that you could be changed of position at any moment, so the competition was always there. What I found funny was that although no one ever dared to complain about always being placed in the back, you could tell how much it bothered all of the girls; there was always a sense of envy running through the room. And although the sense of competitiveness could be overwhelming at times, it taught me to compete with no one but myself. It taught me to focus on always setting the bar above my own expectations, not those of other people. If I wanted to dance, I had to dance for myself before dancing for anyone else.