Studies have shown that red creates submissive behavior in those who are exposed to it. A red tutu, then, helps the wearer stand out in a crowd where other calmer colors, such as blue and green, are prevalent and lend an advantage in competitive settings, such as dance competitions.
A study published in Psychological Science, the journal of the Association of Psychological Science, found that a species of monkeys in Puerto Rico avoided scientists in red who placed apple slices out for them to eat. But when scientists wore other colors, such as blue and green, the monkeys took the food. These differing behaviors, combined with the dominance of athletes who wore red in the 2004 Olympics, led the author of the study to conclude humans have a natural biological aversion to the color. If an advantage in a competition is sought, a red tutu is the best color to use.
In the world of fashion, red is used because it's bold and stands out. Red was for a long time the color of royalty and signified wealth and abundance. When wearing a tutu in a casual environment, red commands attention and is good for someone who either is or wants to be the center of attention.