That Umbrella became a Tsukumogami, after its owner Ai Kasahara left it by accident.
Its owner Ai was in love with a student named Omoi Kata, and hoped to share her umbrella with him whenever it rained since he did not have one, but was too shy to ever speak to him. One day, she left that umbrella on a train by accident, and all her unrequited desires turned it into a Tsukumogami, as she had been holding it while longing to share it with him, and it created an illusion of herself and wandered around looking for her unrequited love. It would show up to many male students, offering to share her umbrella and then smack them upon learning he is not the guy she’s looking for and go floating away in the sky, causing Ai to be chastised by those students. Rinne tracked it to show that its owner did manage to date her crush, but much to everyone’s surprise it attacks Ai, asking her what she’s doing with another umbrella, for it also turns out that it wanted the guy to itself.