The progression from butterfly to leaf suggests grasping at the "fundamentals" of something: the butterfly started from a catepillar eating a leaf. However, this idea of progressively digging deeper does not really explain the monologue progression. For instance, with Shiori, the progression is from:
- Always hated Juri and wanted to take something away from her. ("Go deeper.")
- Juri's kindness looked like she was making fun of Shiori. She thought taking away Juri's purported love interest would change things, but she only felt worse after doing so. Now she knows about the pendant, things are different.
- In a good way, Shiori doesn't know what she should do now.
- "It's no use. Why do you look at me like that?"
We do not as a general rule get increasingly "deeper" motives as the background image progresses. The main rule that governs how the monologue progresses seems to be:
- Before "go deeper", consists of at least an allusion to some fears
- After "go deeper", consists on an expansion on the fears and possible explanation of motives.
So while I would not read too much into the stylised elements (which is my general policy with fiction, when the meanings are not obvious), I can say that it at least fits for two reasons:
The butterfly "degrades" into what it is made up of, similar to how we learn what is behind characters' problems.
The progression of the image makes sense because it follows a pattern and isn't blatantly out of place. In a lot of fiction, the exact "meaning" of motifs or stylised elements will never be suggested; the important thing is that they will nonetheless not be out of place.
(To be honest, I think the opposite progression---leaf to butterfly---wouldn't be out of place were all of the segments replaced with that, and if that happened, I would have been able to make something up about how the characters are expanding and developing their motives.)