Aha, so that's it. So she has a crush on Ji-ho (silver hair) and is likely aware that Ji-ho likes Dan-I. So out of jealousy, she tries to isolate and remove Dan-I and try to insert herself into the group so that she can get Ji-ho to like her.
Overall, how wonderful of Dan-I. Absolutely love her. She was nearly overtaken by the rumors, but having the support of her friends is what makes her able to stand so strong. And like she said, if they believed in such petty rumors, then they weren't really her friends at all.