Arlecchino and Columbina got into a fight because of rumors going around that Arlecchino is a traitor to the fatui, and another rumor is she's having an affair with Furina

Arlecchino: Why can't you just believe me!

Columbina: Cause you've been so distant, and I've seen a lady named Furina sending letters to you! So I'm done!