Firstly, the haori is taken off to signify that the story is progressing from the makura (a related topic, or the background to the story, which serves as an introduction to the performance) to the main topic.
まず、演目のイントロダクションともいうべき関連した話題や背景を紹介していく枕から本題に移行する合図として、羽織を脱ぐ。